AMERICAN SOCIETY OF CIVIL ENGINEERS. 






The Results of Investigations Relative to Formula: 
for the. Flow of Water in Pipes. 



By EDMUND B. WESTON. 



WITH DISCUSSION 




By Rudolph Hering, Charles E. Emery, E. Sherman Gould, 
Mansfield Merriman, John R. Freeman and Edmund B. Weston. 









4153 




Ccm^limsnts o) 



Ru^pij^h Hiring, 



Civil EnginKr, 



277 Pearl St. , Lew York. 



rhilnrl^ljih i n, pn . 




r 



<o~l3°/oi) 







AMERICAN SOCIETY OF CIVIL ENGINEERS. 

IN STITUTED 1852. 



TEA N S ACTIONS. 

Note. — This Society is not responsible, as a body, for the facts and opinions advanced in 

any of its publications. 



431. 

(Vol. XXII.— January, 1890.) 



THE EESULTS OF INVESTIGATIONS RELATIVE 
TO FORMULAS FOR THE FLOW OF WATER 
IN PIPES. 



By Edmund B. Weston, M. Am. Soc. C. E. 



WITH DISCUSSION. 



INTBODUCTOKY. 

About thirteen years ago, when the writer first commenced to make 
a practical application of hydraulic formulas, he was unable to find one 
for calculating the loss of head due to the friction of water flowing in 
pipes, which he had not heard criticised more or less unfavorably by 
hydraulic engineers. 

This unsatisfactory state of affairs led him to commence to make 
special investigations upon the subject, and to collect original data of an 
experimental nature relating to the same, in order to prove to his own 
satisfaction, if possible, if any of the formulas that he was familiar with 
were reliable for general use, and if not, to endeavor to construct one. 

The results of these researches, which are illustrated by sketches and 
diagrams, are now presented in this paper. 

The data of five hundred and twenty experiments were obtained, 
which are tabulated in a systematic manner in Table No. 1. 

A careful study of the experimental data convinced the writer that 
the same formula would not apply to all cases, and that in order to make 



2 WESTOK ON FLOW OF WATER 1^ PIPES. 

an intelligent investigation, it would be necessary to divide it into the 
three following classes, viz. : that which had been obtained with pipes 
having very smooth interior sides similar to brass and lead pipes, that 
which had been obtained with pipes having interior sides similar to new 
cast-iron pipes, and that which had been obtained with pipes having 
interior sides similar to old cast-iron pipes whose interior sides had be- 
come roughened by oxidation. 

The result of this division was the construction by the writer of anew 
formula for the flow of water in pipes having very smooth interior sides, 
and his coming to the conclusion that two formulas constructed by the 
eminent French Civil Engineer, Henry Darcy, were very well adapted for 
pipes having interior sides similar to new cast-iron pipes. 

A. general formula was not found that would satisfactorily apply to 
old cast-iron pipes having interior sides that had become roughened 
by oxidation, and it was not possible to construct one from the limited 
data at hand, although a formula by Darcy, and several by the' writer 
constructed for individual cases, agree very well with the experimental 
results from which they were derived. 

The writer also briefly discusses the form of formulas the best adapted 
for the flow of water in pipes, and calls attention to formulas for com- 
puting the co-efficients of resistance, for enlargements, contractions, 
elbows and curves. 

The investigations and subjects that this paper treats upon will 
hereafter be referred to, or described in detail in the following order : 

First. — The Nomenclature. (Page 3. ) 

Second. — The form of Formulas best adapted for the Flow of Water 
in Pipes. (Page 4.) 

Third.— -The Co-efficient of Influx. (Page 7.) ' 

Fourth. — Description of Table No. 1. (Page 8.) 

Fifth.— Table No. 1. (Page 11.) 

Sixth. — Description of the apparatus used in making the experiments, 
the results of which are contained in Table No. 1. (Page 23. ) 

Seventh. — A Formula for the Flow of Water in Pipes having very 
smooth Interior Sides. (Page 48. ) 

Eighth. — Formulas for the Flow of Water in Pipes having Interior 
Sides similar to New Cast-Iron Pipes. (Page 56.) 

Ninth. — Old Cast-Iron Pipes Lined with Deposit, and the same 
cleaned. (Page 60.) 

Tenth. — The Co-efficients of Eesistance to the Flow of Water in 
Pipes, for Enlargements, Contractions, Elbows and Curves. 
(Page 61.) 



WESTON" ON FLOW OF WATER IN PIPES. 3 

NOMENCLATIVE. 

Unless distinctly stated to the contrary, the following characters will 
always represent English feet when they apply to linear distances, and 
have these significations : 

7^ = the head. When the pipe is submerged, it is the difference 

in elevation between the surface of the water at the inlet 

and outlet; or when the pipe discharges into the open air, 

it is the difference in elevation between the surface of the 

water at the inlet, and the center of the outlet end of the 

pipe. 
h /. = the loss of head due to friction, of the water flowing against 

the interior sides of the pipe, etc. 
I = the length of the pipe. 
d = the mean interior diameter of the pipe. 
g = the acceleration of gravity. 
v = the mean velocity, per second, of the water flowing in the 

pipe, or the velocity, per second, of the water issuing from 

the outlet end of the pipe. 
£ = the co -efficient of influx or resistance of the entrance of the 

water into the pipe. 
A = the coefficient of contraction of the entrance of the water 

into a pipe. 
£ = the co-efficient of friction of the water flowing against the 

interior sides of the pipe. 
cp = the co-efficient of resistance of the water passing from a large 

to a small pipe. 
(.1 = the co-efficient of resistance of the water passing from a 

small to a large pipe. 
F = the area or cross section of a pipe. 
xp = the co-efficient of resistance of the water flowing in a curved 

pipe. 
r = radius of curvature of a curved pipe. 
r = the co- efficient of resistance of the water flowing in an elbow 

pipe. 
ft = angle of an elbow pipe. 
m = the total number of discharge pipes that are supplied by the 

single pipe under consideration. 
a = an experimental derivation. 
ft = an experimental derivation. 
z = a diametric co-efficient. 
J =z the sine of the inclination of the water surface, or fall in a 

length of 1 (used only inKutter's formula). 
n = the co-efficient of roughness dependent upon the surface of 

the material over which the water flows (used only in 

Kutter's formula). 
oo = a variable co efficient. 
b 
c 
e 
k 
o 
P 

X 

y 



>- charactei-s of Figures Nos. 1 and 2. 



4 WESTON" ON FLOW OF WATEK IN PIPES. 

THE FORM OF FORMULAS BEST ADAPTED FOR THE FLOW 

OF WATER IN PIPES. 

The experience of quite a number of years in solving hydraulic prob- 
lems, has led the writer to the conclusion that the forms of formulas 
most convenient for ascertaining the different results generally sought 
after, relating to the flow of water in straight pipes, are'the following: 

VWhf 



4 



' l/2 g h 



V = 



i +"«+«4 



N 

It is assumed in these forms of formulas that the loss of head due to 
friction increases at the same time with the square of the velocity (t? 2 ), 
and with conditions that are included in the co-efficient of friction C> 
of the water flowing in the pipes. This co-efficient of friction, which is 
an experimental derivation, is not expressed individually in the majority 
of the formulas that have been published by different authorities who 
have made investigations upon the flow of water in pipes, nor is its value 
the same in these formulas, nor the laws upon which it is based. For 
instance, among the formulas that the writer is conversant with, in 
addition to being dependent upon the nature of the interior sides of the 
pipes, there are several in which it is dependent upon the velocity (v), 
one in which it is dependent upon the square root of the velocity (-y/^T), 
one in which it is dependent upon the diameter (d) and one in which 
it is dependent upon both the velocity and diameter, etc. 

The following are several of the different forms of formulas that are 
often met with in hydraulic text books : 

lif = (av +/ 3v2 ^)d' 

I v 2 

f go 2 d 



h*d 



WESTON" ON FLOW OF WATER IN" PIPES. 5 

These forms of formulas are undoubtedly a little more convenient 
for solving very simple problems relating to straight pipes, than are 
those recommended by the "writer; but they cannot be utilized with- 
out a considerable modification for solving the more complicated 
problems that sometimes arise in practice, such as the flow of water 
from a reservoir, through a straight pipe, a compound pipe, or a 
comjDound system of pipes; whereas the forms of formulas, recom- 
mended by the writer, can each be readily extended to cover a great 
variety of cases of this kind, as they contain all of the elements plainly 
set forth that are necessary for calculating the flow of water in pipes, 
with the exception of a little supplementary data, such as the co-effi- 
cients of resistance for contraction, enlargement, elbows and curves, 
which can easily be obtained and introduced when necessary. Then 
there is always a great advantage in having before you individually the 
co-efficient of friction C, which is practically the only important ele- 
ment in a formula, concerning the pipes themselves, that is determined 
by experiment, and upon which almost entirely depends the conversion 
of the theoretical head or velocity into the actual. 

The co-efficient of friction C> as expressed in the formulas recom- 
mended by the writer, has been adopted for the reduction of all the 
experimental data contained in this paper, as well as for the basis 
of all formulas that have been constructed and all comparisons that 
have been made, relative to the flow of water in pipes. 

The following equations illustrate the manner in which the formulas 
recommended can be extended to cover a number of cases. For facility 
of comprehension, the examples to which the different equations apply, 
are expressed by sketches (without regard to scale). 

These sketches are intended to represent plans of different pipes, 
and combinations of pipes, all of which are supposed to be located 
below the hydraulic grade line. 

Example No. 1. 



V* g h 



1 



v-"('+<-t)-£> 



WESTON" ON FLOW OF WATER IN PIPES. 

Example No. 2. 



V*g h 



J^(-+^)(i) 4 +(^.+^)(4J+*+^ 



Z, <#, C s and # refer to the discharge pipe. 
Z 1? c?!, <pi and Ci refer to pipe 1. 
l 2 , d 2 , £ and C 2 refer to pipe 2. 

Example No. 3. 




-/2oA 



J i +0+^i)(i) 4 - 2 +^+^^- 



v-co+^-i)^) 



4 m 2 + 0+c4-_ 



d J 2<T 

ra = the total number of small discharge pipes." 

I, d, <p t C and v refer to one of the small discharge pipes, their 
dimensions all being the same. 
lx, d 1} e and Ci refer to pipe 1. 

Example No. 4. 




WESTON" ON" FLOW OF WATER IN" PTPES. 



V *gh 



+ C 



d 



vH:(-+^)(^-'+(^+^)(-i)- , +*+«4-]^ 

?ra =: the total number of small discharge pipes. 

/, rf, 0, £ aud v refer to one of the small discharge pip2S, their 
dimensions all being the same. 
l\, dn (pi and Ci refer to pipe 1. 
l 2 , (h, £ and C2 refer to pipe 2. 

Example No 5. 




V* 9 h 



^•+«-iK-4)V--+(^+«.i)(-i)-'+^^ 
vH:(' +& i)-<i) I ->*+(*'+ e : i)(i)- ,+ ^r]f, 

m = the number of 3mall discharge pipes that are connected with 
one of the branch pipes. 

m 1 = the number of branch pipes. 

I, d, <p, C and v refer to one of the small discharge pipes, their 
dimensions all being the same. 

hi d x , 0! and Ci refer to one of the branch pipes, the dimensions of 
both being the same. 

/ 2 , d 2 , £ and C 2 refer to pipe 2. 

THE CO-EFFICIENT OF INFLUX. 

As a co-efficient of influx, or of resistance, £, to the entrance of the 
water into the inlet ends of cylindrical pipes, when the edges of these 
pipes are square and flush with the face of a wall or partition, was fre- 



8 WESTON ON FLOW OF WATER IN PIPES. 

quently used in computing the experimental co-efficients of friction (Q, 
contained in Table No. 1, the writer will make a few remarks concern- 
ing it before proceeding to describe the table, viz. : 

e= (—. ) — 1 and lip = e— — . 

0.505 is recommended by Weisbach, which is a result deduced from 

experiments made by himself. 
0.513 is derived from the results of experiments made by Michelotte 

with tubes from 0.5 to 3 inches in diameter, under a head of 

water varying from 3 to 20 feet. 
0.456 is derived from the lesults of five experiments made by Castel 

with tubes 0.61 inches in diameter. 
0.539 is derived from the results of five experiments made by Bossut 

with tubes from 0.91 to 1.03 inches in diameter. 
0.484 is derived from the result of an experiment made by Eytelwein 

with a tube 1.02 inches in diameter. 
0.481 is derived from the result of an experiment made by Venturi 

with a tube 1.61 inches in diameter. 
0.469 is derived from the results of approximate experiments made 

by Darcy with pipes from 1.42 to 11.81 inches in diameter. 

The writer considers the co-efficient 0.505, recommended by Professor 
Weisbach, the most reliable. Therefore whenever the co-efficient of 
influx s has been used in this paper, its value was considered as 0.505, 
unless otherwise distinctly specified. 

DESCRIPTION OF TABLE No. 1. 

This table contains the results of five hundred and twenty experi- 
ments, which have been made to ascertain the laws relating to the flow 
of water in pipes. 

In making the experiments fifty-seven different sizes of pipe were 
used, ranging from 0.409 to 90 inches in diameter, and from 12 feet to 
60,000 feet in length, which were constructed of tin, zinc, brass, glass, 
lead, sheet-iron, artificially coated and not coated, wrought-iron, new 
and old, cast-iron, new &nd old, artificially coated and not coated, wood, 
earthenware and brick. 

The first column contains the tabular numbers of the experimental 
results. 

The second column contains the mean diameter of the interior of 
the pipes. 

The third column contains the heads, which are in all cases the total 
heads, unless they are indicated by *, when they are the friction al 
heads, due to the water flowing against the interior sides of the pipes. 

The fourth column contains the lengths of the pipes. When the 
total head is given in the third column, opposite to it, in this column, 
is given the entire distance from the inlet to the outlet of the pipe; this 



WESTON OX PLOW OF WATER IN" PIPES. 9 

is also the case if the Motional head is given, provided the loss of head 
due to the entrance of the water into the pipe, and the head required to 
generate the velocity, have simply been subtracted from the total head; 
but if manometric tubes, or substitutes for the same, were used in deter- 
mining the head, the length given is the distance between the points 
where the tubes were connected to the pipe. 

The fifth column contains the mean velocity of the water that was 
flowing in the pipes. 

The sixth column contains the co-efficients of influx, or of resistance, to 
the entrance of the water into the pipes, if any were required, that were 
used in computing the co- efficients of friction (£), given opposite in the 
seventh column. When the frictional head is given in the third column, 
the co-efficient of influx does not enter into the problem. If, on the 
contrary, the total head is given, a co-efficient of influx was necessarily 
always employed, if the pipes did not have funnel shaped inlets, and 
in cases where one had not been determined by experimental investiga- 
tion, 0.505 was used for reasons that have already been explained. 
Consequently if 0.505 is given in the sixth column, it is to be under- 
stood that it is an assumed value, and when other values are given it 
implies that they have been determined by experiment to meet the 
requirements of their respective cases. 

The seventh column contains the co-efficients of friction (£), which 
have been computed from the results of the experiments contained in 
the table. When the frictional head was used, the equation employed 
for the determination of the co-efficient of friction (£), was 

_ 2g hf d 

^~~~^~~ T ; 

but when the total head was used, the head required to generate the 
velocity and the loss of head due to the entrance of the water into the 
pipe, had to be considered, and when the co-efficient of influx was 
assumed to be 0.505, the equation employed for a case of this kind was 



-.(111 



1.505 )*. 



The values of 2g, that were used in the computations, have ranged 
between 64.326 and 64.4, depending upon the locality where the experi- 
ments were made. All of the experimental co-efficients of friction (C) 
given in this column may be used in the equation, 

d 2g' 

and in the other equations previously mentioned and recommended by 
the writer ; so that should an instance arise in which any of the for- 
mulas that will be given in this paper, in the future, do not apply, the 
table can be referred to, and quite possibly an independent experimental 



h f =C . 



10 WESTON ON FLOW OF WATER IN PIPES. 

co-efficient of friction (Q can be found, which will exactly '.fill the require- 
ments of the case. 

The eighth column contains the names of the authorities under 
whose direction the experiments were made or published, and the 
nature of the pipes that were used. 

The ninth column contains the numbers of the diagrams upon which 
the co-efficients of friction (C) are platted that were used by the 
writer in determining his formula, and those upon which other co-effi- 
cients of friction (C) have been platted for comparison with formulas of 
different authorities. 

There are quite a number of experimental results given in the table, 
which have not been platted on the diagrams nor mentioned in any form 
outside of the table, as they were not deemed sufficiently reliable, with 
the exception of those which were obtained from experiments that were 
made with wooden pipe, which were not required. These results can be 
ascertained by referring to the ninth column, as the space opposite to- 
them in this column will not contain a diagram number. 



WESTON OK FLOW OF WATER IK PIPES. 
TABLE No. 1. 



1: 



Experimental Values of the Coefficients of Friction (C) of Water in- 
Pipes of Different Sizes, the Data^froni which they were Obtained, 
and the Number of the Diagram on which they are Platted. 



No. 



S ° 
A 



0.409 



0.563 



0.480 



0.500 



0.502 



0.551 



4f 

0. 28 

0.60 

1.00 

1.75 

2.47 

5.44 

8.47 

11.39 

14.43 

20.55 

28.07 

58.60 

112.95 



0.82 
1.27 
2.16 
3.03 



0.10 

0.55 

1.41 

4.14 

10.08 

18.76 

26.49 



328.09 



15.00 



11.13 



164 



05 



<x> 
® . 

o a> 



0.62 

0.63 

0.70 

1.87 

6.63 

27.92 

28.35 

40.42 

68.87 

0.73 

28.41 

33.40 

40.68 

70.84 



0.11 
0.23 
0.38 
0.48 
0.55 
0.75 
0.94 
1.13 
1.29 
1.57 
1.88 
2.78 
3.92 



2.35 
5.13 



2.08 
2.72 
3.66 
4.44 



0.13 
0.54 
0.81 
1.46 
2.40 
3.44 
4.23 



a 

© . 

a 



0.505 



0.488 



t 



0.0527 
0.0676 
0.0498 
0.0365 
0.0273 
0.0182 
0.0187 
0.0178 
0.0169 
0.0607 
0.0172 
0.0187 
0.0174 
0.0148 



0.1719 
0.0869 
0.0532 
0.0590 
0.0632 
0.0751 
0.0750 
0.0706 
0.0685 
0.0656 
0.0624 
0.0597 
0.0577 



0.0283 
0.0230 



0.0404 
0.0361 
0.0335 
0.0316 



0.1099 
0.0339 
0.0391 
0.0349 
0.«315 
0.0286 
0.0267 



Name of the Experimenter, 
etc., and Nature of the 
Pipe. 



Brass 
Brass 
Brass 
Brass 
Brass 
Glass 
Brass 
Brass 
Brass 
Glass 
Brass 
Glass 
Brass 
Brass 



Weisbach. 

Pipe 

Pipe 

Pipe , 

Pipe 

Pipe ■ 

Pipe 

Pipe 

Pipe 

Pipe 

Pipe 

Pipe 

Pipe 

Pipe 

Pipe ■ 

Dakcy. 



j-New wrought-iron pipe. 



Reknie. 



> Lead pipe 

Smith. 



[•Glass pipe 

J 

Dakcy. 



[■New lead pipe. 



land 7 
1 and 7 
1 and 7 



land 7 
laud 7 
1 and 7 
1 and 7 
land 7 
1 and 7 
1 aDd 7 
1 and 7 
land 7 



25 
25 
25 
25 
25 
25 
25 
25 
2o- 
25- 
25 
25 
25 



1 

1 and 7 
land 7 
1 and 7 
1 and 7 
1 and 7 
1 and 7 



* The heads of this authority are those due to friction only. 



12 



WESTON ON" FLOW OF WATER IN" PIPES. 
TABLE No. 1— ( Continued. ) 





a 


\o. 


1 i 
as 


41 


0.628 


4*2 




43 




44 




45 




46 




47 


0.746 


48 


" 


49 


<< 


50 


Cl 


51 


0.969 


52 


0.972 


53 




54 




55 




56 




57 




58 


1.000 


■ 59 


1.020 


^0 


" 


61 


1.047 


62 


«« 


83 


<■ 


64 


<« 


65 


" 


66 


« : 


67 


it 


■68 


n 


69 


" 


70 


tt 


71 


*t 


73 


(i 


74 


(< 


75 


«« 


76 


«« 


77 


" 



0.81 
1.71 
3.31 

4.87 
6.59 
8.35 



0.67 
2.06 
3.66 
5.07 



121.10 



150.00 



11.13 

20.80 



0.07 

0.08 

0.08 

0.11 

0.18 

50 

1.60 

3.33 

- 6.36 

6.26 

14.27 

20.72 

22.88 

34.68 

58.49 

83.99 

101.55 



60 



13 



34.94 



781.80 



100.00 



9.29 
19.20 



328.09 



" a 

a o 

•fi o 

° ft 



1.03 
1.58 
2.30 
2.86 
3.39 
3.88 



1.40 
2.65 
3.67 
4.37 



6.03 



0.68 
0.79 
10.47 
15.52 
20.47 
30.12 



21.70 



14.58 
15.67 



0.12 
0.13 
0.13 
0.19 
0.28 
0.43 
0.81 
1.21 
1.71 
2.19 
2.61 
3.15 
4.05 
4.20 
5.52 
6.56 
7.17 



O 



3 3 

J M 

o 



0.469 



0.488 



0.332 



0.352 



0.4014 
0.0368 
0.0335 
0.0318 
0.0306 
0.0296 



0.0367 
0.0309 
0.0284 
0.0277 



0.0221 



0.0432 
0.0425 
0.0196 
0.0184 
0.0179 
0.0167 



0.0160 



0.0185 
0.0182 



0.0838 
0.0836 
0.0799 
0.0515 
0.0388 
0.0162 
0.0413 
0.0391 
0.0371 
0.0367 
0.0358 
0.0357 
0.0343 
0.0336 
0.0329 
0.0335 
0.0339 



Name of the "Experimenter, 
etc., and Nature of the 
Pipe. 



Smith. 



£ 



}>New gas pipe. 



Smith. 



1 
i 
J- Glass pipe. 



Weston. 

Wrought-iron pipe, lined 
with tin 



Weisbach. 



[-Zinc pipe. 



Hooson. 



Neville. 



Darcy. 



f-New wrought-iron pipe. 



1 and 7 
1 and 7 
1 and 7 
1 an d 7 
1 and 7 
1 and 7 



2 and 9 



2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 



2 and 9 



2 and 9 
2 and 9 



25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 
25 



* The heads of this authority are those due to friction only. 



WESTON ON FLOW OF WATER IN PIPES. 
TABLE No. 1.— (Continued.) 



1.3 



5 M 
ft 



W 



1.054 



1.055 



1.063 



1.066 



1.066 



0.47 
0.79 
1.66 
3.27 
4.85 
6.59 
8.33 



0.07 

0.22 

0.74 

2.00 

3.72 

7.29 

9.1-6 

14.90 

33.87 

59.01 

80.12 

100.77 

07 

0.49 

1.34 

3.72 

8.92 

17.23 

24.00 



0.36 
1.07 



0.01 
0.40 
0.60 
0.37 
0.37 
0.53 
0.69 
0.80 
0.80 
1.09 
1.22 
1.30 
2.10 
0.53 
1.60 
1.86 
2.37 
3.20 



60.17 



328.09 



164.05 



53.27 



65.45 
65.45 
12.30 
12.30 
12.30 
65.45 
65.45 
65.45 
65.45 
65.45 
65.45 
65.45 
65.45 
12.30 
10.39 
12.30 
10.39 
10.39 



a o 



a ft 



0.96 
1.42 
2 15 
3.18 
3.95 
4.67 
5.33 



0.10 
0.30 
0.51 
0.89 
1 26 
1.86 
2.22 
2. 80 
4.81 
6.10 
7.23 
8.22 
0.21 
0.62 
1.09 
1.96 
3.35 
4.72 
5.51 



1.09 
1.98 



0.14 
0.32 
0.77 
0.93 
0.95 
1.18 
1.34 
1.45 
1.48 
1.78 
1.86 
1.94 
2.55 
2.61 
5.18 
5.22 
6.33 
7.54 



■sg 

o 



0.563 



0.505 



0.505 



0.0459 
0.0:-S45 
0.0315 
0.0282 
0.0269 
0.0261 
0.0253 



0.1285 
0.0416 
0.0491 
0.0436 
0.0404 
0.0363 
0.0347 
0.0328 
0.0289 
0.0274 
0.0265 
0.0258 
0.0552 
0.0450 
0.0391 
0.0337 
0.0276 
0.0269 
0.0275 



0.0299 
0.0267 



0.0570 
0.0353 
0.0376 
0.1910 
0.1823 
0.0309 
0.0315 
0.0312 
0.0300 
0.0283 
0.0286 
0.0280 
0.0263 
0.0256 
0.0200 
0.0209 
0.0197 
0.0181 



Name of the Experimenter, 
etc., and Nature of the 
Pipe. 



Smith. 



■ New gas pipe, not tarred. 



Darcy. 



New sheet-iron pipe, 
coated vrith bitumen 



J- New lead pipe. 



Bossut. 



J Lead pipe. 



Dubuat. 



}>Tin pipe. 



2 and 9' 
2 and 9 
2 and 9- 
2 and 9- 
2 and 9 
2 and 9 
2 and 9^ 



2 and 9 
2 and 9^ 
2 and 9 
2 and 9 
2 and 9- 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9* 
2 and 9 



2 and 9 
2 and 9- 



9 
2 and 9 



2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9 
2 and 9- 



*The beads of this autborily are these due to friction only. 



14 



WESTON ON FLOW OF WATER IN PIPES. 
TABLE No. 1.— (Continued.) 



No. 



a 




•|H 
















<D & 


a 


o 

a 
i— i 


ft 





124 


1.25 


125 


" 


12ti 


" 


127 


" 


128 


" 


129 


" 


130 


" 


131 


" 


132 


" 


133 


(i 


134 


*t 


135 


" 


136 


" 


137 


" 


138 


" 


139 




140 


1.26 


141 


" 


142 


" 


143 


" 


144 




145 


1.27 


146 


1.42 


147 


" 


148 


" 


149 


<< 


150 


n 


151 


" 


152 


•' • 


153 


" 


154 




156 




157 


" 


158 


" 


159 


" 


160 


<( 


161 


1.43 


162 


" 


163 


" 


164 


'« 


165 


" 


167 


" 



0.17 
0.23 
0.32 
0.40 
0.52 
0.65 
0.89 
1.21 
J. 51 
1.92 
2.30 
2.54 
2.86 
2.97 
3.92 
5.92 



1.57 
3.31 
4.94 
6.70 
8.52 



1.07 
1.07 
1.07 
2.13 



2.13 

2.13 

8.02 

15.16 

22.29 



0.08 
0.23 
0.60 
2.20 
5.00 
10.63 
13.63 



100.00 



62.05 



191.78 

159.82 

127.86 

191.78 

95.87 

159.82 

63.93 

127.86 

95.87 

31.96 

63.93 

31.96 

62.88 

125.76 

188.64 



328.09 






>> 9 



0.54 
0.65 
0.73 
0.83 
0.96 
1.12 
1.29 
1.52 
1.75 
1.97 
2.25 
2.35 
2.48 
2.52 
2.96 
3.65 



1.65 
2.47 
3.01 
3.52 
3.99 



1.18 



1.12 
1.25 
1.43 
1.68 
1.68 
1.87 
2.07 
2.13 
2.49 
2.94 
3.06 
4.31 
6.14 
6.15 
6.16 



0.15 
0.26 
0.42 
0.81 
1.22 
1.76 
2.02 



•*-< X 

o a 

O r " 1 

O 



0.505 



0.563 



0.505 



r. 



0.0375 
0.0350 
0.0387 
0.0374 
0.0363 
0.0332 
0.0343 
0.0336 
0.0315 
0.0316 
0.0289 
0.0293 
0.Q296 
0.0298 
0.02t5 
0.0282 



0.0599 
0.0564 
0.0567 
0.0562 
0.0556 



0.0343 



0.0331 
0.0314 
0.0^96 
0.0292 
0.0281 
0280 
0.0267 
0.0266 
0.0254 
0.0237 
0.0243 
0.0218 
0.0228 
0.0228 
0.0228 



0.0809 
0.0813 
0.0792 
0.0793 
0.0805 
0.0782 



Name of the Experimenter, 
etc., and Nature of the 
Pipe. 



Sm EATON. 



Smith. 



► Wood pipe. 



Weisbach. 
Zinc pipe 



Bossut. 



>Tin p : pe. 



Daecy. 



[Old cast-iron pipe, lined 
with deposit 



10 
• 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 
3 and 10 



3 and 10 



3 and 11 
3 and 11 
3 and 11 
3 and 11 
3 and 11 
3 and 11 
3 aud 11 
3 and 11 
3 and 11 
3 and 11 
3 and 11 
3 and 11 
3 and 11 
3 and 11 
3 and 11 



26 
2i 
26 
26 
26 
26 



* The heads of this authority are those due to friction only. 



WESTON ON FLOW OF WATER IN PIPES. 
TABLE No. 1.— (Continued.) 



15 







1 




-n 














-^ 


<x> 


Vh 






a 




-U 


<o 


o . 


o 






a 


<B 


<o 


^ -a 


1 






CS 


i 


n • 






.2 § 


c 

45 .: i 


IName of the Experimenter, 


to 


No. ' 


g s 


Pj 


•f-H 


t>> aj 


■3 2 


y 


etc., and Mature of the 


5 


a. ^ 


t3 


si 

-4-> 


X. 05 


£5 


•5' 


Pipe. 


35 


c3 


6D 

a 


c i? 


0/ - 

6~ 






o 


5 


w 




"3 *"* 
> 


a 






o 


1 

1 










| 


Dakcy. 








* 














168 


1.43 


0.23 


328.09 


0.37 




0.0396 


) 


27 


1691 


" 


0.59 


" 


0.62 




0.0363 


i 


27 


170 


" 


2.14 


" 


1.27 





0.0309 


1 


27 


171 


" 


4.73 


" 


1.97 





0.0285 




27 


1721 


" 


9.90 


" 


2.93 


1 


0.0J71 ! 


1 


27 


173 


« 


13.01 


«' 


3.39 





0.0265 i 




27 


171 




15.26 
w ■ 




3.69 




0.0262 I 


J 

Provis. 


27 


175 


1.50 


1.85 


80.00 


2 70 




0.0255 


) 


3 and 11 


170 


'« 


2.09 


" 


3.09 




0.0220 




3 and 11 


177 


" 


1.15 


60.00 


2.46 




0.0255 


■ 


3 and 11 


178 


" 


1.49 


»• 


2.86 




0.0244 




3 and 11 


179 


" 


1.65 


t* 


3.00 




0246 




3 and 11 


180 


«< 


1.83 


" 


3 .20 


0.(240 




3 and 11 


181 


<< 


1.98 


" 


3.34 


0.0238 




3 and 11 


182 


" 


2.15 


" 


3.41 




0.0248 




3 and 11 


183 


t: 


• 2.16 


•• 


3 52 




0.0234 




3 and 11 


184 


'« 


2.32 


" 


3.63 




0.0 k36 




3 and 11 


185 


" 


2.44 


" 


3 77 




0.0230 




3 and 11 


186 


l| 


2.46 


" 


3.77 




0.0232 




3 and 11 


187 


" 


2.64 


«« 


3.95 




0.0227 




3 and 11 


18S 


" 


2.84 


". 


3.97 


... 


0.0242 1 




3 and 11 


189 


«l 


2.92 


" 


4.18 




0.0224 




3 and 11 


190 


tt 


3.13 


-' 


4.32 




0.0225 i 




3 and 11 


191 


tt 


3.40 


«« 


4.56 




0.0219 




3 and 11 


192 


" 


0.55 


40.00 


2.12 


..•<•• 


0.0216 | 




3 and 11 


193 


tt 


0.87 


«■ 


2.66 




0.0247 ! 




3 and 11 


194 


" 


0.90 


" 


2.68 




0.0.52 




3 and 11 


195 


a 


1.16 


" 


3.13 


..«••• 


0.0238 




3 and 11 


• 196 


" 


1.18 


" 


3.16 




0.0238 




3 aud 11 


197 


" 


1.20 


" 


3.18 




D.0239 




.3 and 11 


198 


a 


1.45 


.« 


3.52 




0.0235 | 




3 and 11 


199 


" 


1.46 


« 


3.58 


...•■• 


0.0229 




3 aud 11 


200 


" 


1.49 


'« 


3.58 





0.0234 




3 and 11 


201 


" 


1.50 


'< 


3.64 




0.02*8 




3 and 11 


202 


" 


1.66 


c 


3.90 




0.0219 




3 and 11 


203 


" 


1.76 


'« 


3.93 




0.0229 




3 and 11 


204 


" 


1.77 


'• 


3.98 




0.02.5 




3 and 11 


205 


" 


1.79 


*• 


4.00 




0.0225 




3 and 11 


206 


" 


1.98 


" 


4.25 




0.0220 




3 aud 11 


207 


" 


2.08 


" 


4.35 





0.0221 




3 and 11 


208 


" 


2.03 


•« 


4.37 




0.0214 




3 and 11 


209 


" 


2.31 


(( 


4 59 




0.0220 




3 and 11 


210 


" 


2.38 


'• 


4.66 




0.0220 




3 and 11 


211 




2.6U 


( ( 


4.91 




0.0214 


J 

Dakcy. 


3 and 11 


212 


1.55 


0.07 


328.09 


0.21 




0.0435 


1 


25 


213 


" 


0.26 


" 


0.36 




0.0489 




25 


2U 


" 


0.60 


«"• 


O.til 




0.0413 


• ■ 


25 


215 


<t 


1.10 


" 


0.86 




0.0381 


} New wrought-iron pipe. . 


25 


216 


" 


2.13 


" 


1.25 




0.0. M6 


1 


25 


217 


" 


4.22 


a 


1.84 




0.0318 


' 


25 


218 


a 


7.84 


I 


2.58 




0.0298 


J 


25 



* The heads of this authority are those due to friction only. 



16 



WESTON" OK FLOW OF WATER IK PIPES. 
TABLE No. 1. — (Continued.) 





a 








O 






a 

C3 




Oj EC 


fR 


a 


S 3 


a 




Name of the Experimenter, 


So 


No. 


is 


fl 




j? CO 




c 


etc , and Nature of the 
Pipe. 


5 

1-c 




03 


be 


'S jj 


*> 3 






o 




•5 >-i 


01 


s 


o ^ 


6 ~* 










ft 


w 


0) 

I-} 




O 






d 
















Darcy. 








* 














219 


1-55 


10.25 


323.09 


3.00 




0.0289 


) 


25 


220 




14.27 




• 


3.59 




0.0281 


1 


25- 


221 




40.41 




' 


6.30 




0.0259 


[-New wrought-iron pipe.. 


25 


222 




57.59 




' 


7.56 




0.0256 


1 


25 


223 




73.52 




• 


8.52 




0.0257 


J 




224 


1.61 


0.13 


164 


05 


0.39 





0.0458 


I 


3 and 11 


225 




0.59 






0.91 




0.0382 




3 aud 11 


226 




1.28 




« 


1.40 




0.0342 




3 and 11 


227 




3.79 
9.19 




, 


2.60 
4.32 


...... 


0.0296 
0.0260 




3 and 11 


228 




3 and 11 


229 




18.17 




« 


6.32 




0.0240 




3 and 11 


230 




24.97 




< 


7.56 




0230 


J 


3 and 11 


231 


1.96 


0.14 


147 


.19 


0.50 




0.0399 


] 


4 and 12 


232 




0.51 




« 


1.02 




0.0 i4o 


i 


4 and 12 


233 




1.14 
3.41 




, 


1.59 
2.93 




0.0320 
0.0283 


1 


4 and 12 


234 


i 


4 and 12 


235 




8.48 




« 


4.85 




0.0257 


I 


4 aud 12 


23t5 




16.47 




6.92 




0.0245 


J 

Dr. Robison. 


4 and 12 


237 


2.00 


12.75 


3300.00 


1.24 


0.505 


0.0277 


Bossut. 


4 and 12 


238 


2.14 


1.07 


191.78 


1.45 


0.505 


0.0288 


1 


4 and 12 


239 




1.07 


159.82 


1.63 


" 


0.0273 




4 and 12 


240 




1.07 


127.86 


1.84 


<> 


0.0262 




4 and 12 


241 




1.07 


95.87 


2.11 


" 


0.0258 




4 and 12 


242 




2.13 


191.78 


2.20 


" 


0.0251 


I 


4 and 12 


243 




2.13 


159.82 


2.44 


" 


0.0241 


\ Tin pipe 


4 and 12 


244 




1.07 


63.93 


2.59 


" 


. 0242 




4 and 12 


245 




2.13 


127.86 


2.74 


" 


0.0233 




4 and 12 


246 




2.13 


95.87 


3.18 


" 


0.0225 


i 


4 and 12 


247 




1.07 


31.96 


3.58 




0.0215 




4 and 12 


248 




2.13 


63.93 


3.82 




0221 


j 


4 and 12 


249 




2.13 


31.96 


5.23 




0.0196 


Leslie. 


4 and 12 


250 


2.50 


0.46 


1036.00 


0.22 


0.505 


0.1212 


1 




251 




1.45 




' 


0.72 


" 


0.0347 




4 and 13- 


252 




2.78 




• 


1.09 


■" 


0.0289 




4 and 13 


253 




4.76 




< 


1.47 


" 


0.0271 




4 and IS 


254 




7.01 




« 


1.73 


«' 


0.0288 




4 and 13 


255 




9. 9 J 




• 


2.10 


" 


0.0278 




4 and 13 


256 




1.01 


540 


00 


0.58 


" 


0.0748 






257 




1.78 






0.'-9 


" 


0.0699 






258 




2.50 
5.50 




, 


1.07 
2.21 


,, 


0.0541 
0.0273 




4 and 13 


259 




4 and 13. 


260 




8.48 




< 


2.93 


" 


0.0239 




4 and 13 


261 




9.99 




< 


3.35 


" 


0.0215 




4 and 13 


262 




0.17 


270 


00 


0.34 


" 


0.0700 






263 




2.47 




< 


2.26 


" 


0.0229 




4 and 13 


264 




5.44 




' 


3.26 


" 


0.0243 




4 and 13 


265 




10.14 




« 


.4.89 


" 


0.0199 


s 


4 and 13 


266 




0.19 


100 


00 


0.86 


" 


0316 


. 


4 and 13 



4 * The heads of this authority are those due to friction only. 



WESTOK OK FLOW OF WATER IK PIPES. 
TABLE No. 1.— (Continued.) 



17 



No. 


PI 

•iH 

-2 <D 

IS 

£ M 
ft 


CD 

•i-t 


Length in Feet. 


-*3 

CO 

®_; 

• rH o 
>>© 

^QQ 
'« U 

O CD 
•—< Q. 

CD " 
> 


=4-1 

o 
a 

CD • 

® a 
O 


» 


tfame of the Experimenter, 
etc., and Nature of the 
Pipe. 


a 

c3 

U 

to 
a 

S 

o 

d 
















Leslie. 




267 


2.50 


4.36 


100.00 


4.89 


0.505 


0.0213 


) 


4 and 13 


v>68 


<« 


6.61 

8.25 


ii 

tt 


6.01 
6.90 


» 


0.0214 
0.0201 




4 and 13 


269 




4 and 13 
















Dakot. 








* 














270 


3.15 


0.21 


328.09 


0.40 




0.0693 


| 


26 


271 


it 


0.82 


" 


0.81 




0.0641 




26 


272 


f c 


2,38 


ii 


1.44 




0.0589 


h Old casMron pipe, lined 


26 


273 


If 


5.28 
10.17 


tt 


2.19 
3.01 




0.0568 
0.0580 


26 


274: 




26 


275 


II 


14.88 


tt 


3.69 




0.0564 


J 


26 


276 


CI 


0.28 


tt 


0.63 




0.0358 


1 


27 


277 


II 


0.96 


tt 


1.26 




0.0314 




27 


278 


II 


2.37 


n 


2.01 




0.0301 


| 


27 


279 


(I 


2.42 


tt 


2.05 




0.0299 




27 


2*0 


II 


5.11 


tt 


2.83 




0.0328 


1 


27 


281 


" 


9.64 


" 


4.09 




0.0299 


1 


27 


282 


" 


14.68 


ii 


5.01 




0.0304 


i 


27 


283 


3.22 


0.07 


it 


0.29 




0.0418 


1 


15 


284 


" 


0.27 


«' 


0.56 




0.0453 




15 


285 


u 


0.76 


«« 


1.17 




0.0291 




15 


286 


i< 


1.74 


i< 


1.84 




0.0271 




15 


287 


" 


3.35 


«« 


2.59 




0.0262 




15 


288 


" 


7.40 


«i 


3.89 




0.0258 




15 


289 


ii 


10.53 


ii 


4.65 




0.0256 




15 


290 


n 


13.26 


ii 


5.15 




0.0263 




15 


291 


" 


31.32 


ii 


8.05 




0.0255 




15 


292 


" 


32.49 


" 


8.16 




0.0257 




15 


293 


" 


39.30 


ii 


8.92 




0.0260 




15 


294 


" 


55.14 


«i 


10.62 




0.0258 




15 


295 


" 


56.01 


«« 


10.71 




0.0257 




15. 


296 


3.25 


0.09 


ii 


0.33 




0.0438 


1 


5 and 14 


297 


" 


0.22 


ii 


0.58 




0.0345 




5 and 14 


298 


ii 


0.67 


*.« 


1.17 




0.0258 




5 and 14 


299 


ii 


2.06 


ii 


2.18 




0.0231 


i 


5 and 14 


300 


ii 


4.00 


«< 


3.12 




0.0219 




5 and 14 


301 


ii 


7.50 


tt 


4.44 




0.0202 


! New sheet-iron pipe, coat- 


5 and 14 


302 


ii 


10.19 


" 


5.29 




0.0194 ' 


5 and 14 


303 


ii 


13.35 


tt 


6.15 




0.0188 




5 and 14 


304 


ii 


23.52 


n 


8.44 




0.0176 




5 and 14 


305 


ii 


34.96 


tt 


10.53 




0.0167 




5 and 14 


306 


tt 


45.54 


ti 


12.03 




0.0167 




5 and 14 


307 




51.20 


tt 


12.79 




0.0167 


) 

Jabdine. 


5 and 14 


308 


4.50 


51.00 


14930.00 


1.71 


0.505 


0.0282 




















Couplet. 




309 


5.33 


0.50 


7481.66 


0.18 


0.505 


0.0593 


1 

• Stoneware and lead pipe. 


16 


310 


<i 


1.01 


ii 


0.28 


«« 


0.0489 


16 


311 
312 


ii 
<i 


1.49 

1.87 


ii 
ii 


0.37 
0.43 


ii 
tt 


0.0422 
0.0391 


16 
16 


313 


ii 


2.13 


ic 


0.46 


" 


0.0379 




16 


314 


ii 


2.22 


tt 


0.47 


" 


0.0378 


J 


16 



*The heads of this authority are those due to friction only. 



18 



WESTON ON FLOW OF WATER IN" PIPES. 
TABLE No. 1— (Continued.) 







+» 


•*s 


4> 


O 






a 




a 


a> 


.2 


fnr} 


-U 






H 






h 


.2 § 






Name of the Experimenter, 


o3 


No. 


""o 


a 


>> <o 


■3g 


t. 


etc., and Nature of the 


A 




S3 


13 






8<rt 




Pipe. 


o 




3 




a 

1-1 




6 M 






© 
















Darct. 




315 


5.39 


0.08 


328.09 


0.49 




0.0292 


1 


16 


316 


a 


0.29 


«« 


0.98 




0.0263 




16 


317 


n 


0.69 


t t 


1.60 


• ••• • • 


0.0236 




16 


318 


<< 


1.56 


a 


2.50 




0.0220 




16 


319 


a 


4.13 


«< 


4.19 




0.0208 




16 


320 


«« 


7.30 


it 


5.62 




0.0204 




16 


321 


>i 


10.89 


«« 


6.88 




0.0203 




16 


322 


«< 


12.81 


n 


7.48 




0.0202 




16 


323 


<< 


32.32 


tt 


11.94 




0.0200 




16 


324 


a 


54.98 
* 


tt 


15.39 




0.0205 


Weston. 


16 


325 


6.00 


21.19 


1170.90 


4.70 




0.0264 


j Cast-iron pipe, coated 


16 


32fi 


•< 


47.64 


tt 


7.25 




0.0249 


16 


327 
328 


" 


65.46 


a 


8.49 




0.0249 


V with coal-tar, in service 


16 
16 




73.16 




9.26 




0.0234 


















Dakoy. 








* 














329 


7.40 


0.09 


328.09 


0.65 




0.0251 


1 


17 


330 




0.67 


tt 


1.64 




0.0259 


» 


17 


331 




1.21 


a 


2.50 




0.0233 




17 


332 




2.64 


n 


3.72 




0.0231 




17 


333 




4.40 


ti 


4.90 




0.0221 




17 


334 




7.38 


it 


6.37 




0.0220 




17 


335 




12.50 


" 


8.25 




0.0221 




17 


336 




36.02 


•* 


14.23 




0.0215 




17 


337 




47.87 


'• 


16.23 




0.0219 




17 


338 


7.72 


0.07 


" 


0.59 




0.0237 


] 


23 


339 




0.16 


tt 


0.91 




0.0239 




23 


340 




0.42 


it 


1.53 




0.0228 




23 


341 




1.08 


" 


2.56 




0.0209 




23 


342 




1.90 


ii 


3.53 




0.0193 




23 


343 




3.90 


ii 


5 44 




0167 


New sheet-iron pipe, 


23 


344 




3.94 


it 


6.51 




0.0164 


coated with bitumen. 


23 


345 




6.89 


it 


7.41. 




0.0158 


< 


23 


346 




9.74 


»« 


9.00 




0.0152 




23 


347 




11.94 


" 


10.01 




0.0150 . 




23 


348 




39.88 


" 


19.72 




0.0129 




23 


349 


9.63 


0.31 


i« 


1.00 




0.0489 


) 


26 


350 




0.66 


'• 


1.46 




0.0487 




26 


351 




1.55 


it 


2.29 




0.0465 




26 


352 




3.77 


•' 


3.58 




0.0463 


Old cast-iron pipe, lined 


26 


363 




7.51 


it 


5.01 




0.0471 


26 


354 




10.50 


a 


5.94 




0.0468 




26 


355 




13.47 


ii 


6.72 




0.0470 




26 


356 




45.87 


ii 


12.42 




0.0468 




26 


357 




0.17 


ii 


0.91 




0.0316 




27 


358 




0.54 


ii 


1.76 




0.0275 


1 


27 


359 




1.63 


ii 


3.11 




0.0266 


1 


27 


360 
361 




3.79 
6.68 


ii 


4.66 
6.25 




0.0274 
0.0269 


i 


27 
27 


362 




8.97 


tt 


7.24 




0.0270 


1 


27 


363 




12.24 


tt 


8.44 




0.0271 


1 


27 


364 




37.22 


tt 


14.75 




0.0269 


J 


27 



* The heads of this authority are those due to friction only. 



WESTON OK FLOW OF WATER IK PIPES. 
TABLE No. 1— {Continued.) 



19 



® r3 

!§ 

ft 



10.93 



11.22 



11.69 



12.00 



12.05 



12.67 



6.56 
10.20 
12.85 
19.01 
24.22 



*. 

0.23 
0.84 
1.42 
2.25 
3.90 
6.71 
9.21 
0.09 
0.39 
0.88 
1.76 
3.63 
7.56 
10.52 
13.47 



4.00 
19.00 
16.75 
40.00 
38.00 

5.50 
12.00 
18.00 
24.75 
27.00 
34.50 
46.00 



21.30 
21.30 
34.40 
32.80 
47.60 
45.90 
64.00 
69.70 



5.13 
10.89 
16.69 
24.51 



730.60 
721.30 
713.90 
697.00 
684.80 



328.09 



a o 



5200.00 



8140.00 



6600.00 



17684.00 



718.40 
709.20 
699.60 
684.90 



4.76 
6.12 
6.95 
8.69 
10.05 



1.30 
2.78 
3.87 
4.90 
6.67 
8.85 

10.52 
0.80 
1.76 
2.71 
3.79 
5.42 
7.84 
9.18 

10.37 



1.45 
2.91 
2.91 
4.35 
4.35 



<p pi 



3.57 
4.11 



1.55 
1.57 
2.10 
2.12 
2.60 
2.62 
3.10 
3.13 



4.61 

6.98 

8.68 

10.76 



0.505 



0.0219 
0.0209 
0.0206 
0.0198 
0.0192 



0.0251 
0.0198 
0.0174 
0.0172 
0.0161 
0.0157 
0.0153 
0.0275 
0.0240 
0.0229 
0.0235 
0.0238 
0.0236 
0.0239 
0.0240 



0.0232 
0.0276 
0.0243 
0.0259 
0.0246 
0.0213 
0-0264 
0.0291 
0.0305 
0.0304 
0.0263 
0.0277 



0.0322 
0.0317 
0.0284 
0.0267 
0.0257 
0.0244 
0.0244 
0.0227 



0.0213 
0.0199 
0.0200 
0.0194 



Name of the Experimenter, 
etc., and Nature of the 
Pipe. 



Smith. 



I Riveted sheet-iron pipe, 
Y coated with coal-tar and 
J asphaltum 



Darct. 



! New sheet-iron pipe, 

coated with bitumen. 



Old cast-iron pipe, thor- 
oughly cleaned 



Simpson. 



I Cast-iron pipe, in service 
less than seven years. 



Cast-iron pipe, no record 
of service 



Cast-iron pipe, in service 
less than 4 years 



Bonn Water Works. 



I New cast-iron pipe, coated 
[ with asphaltum 



Smith. 

(Riveted sheet-iron pipe, 
coated with coal-tar and 
asphaltum , 



18 
18 
18 
18 
18 



24 
24 

24 
24 
24 
24 
24 
18 
18 
18 
18 
18 
18 
18 
18 



18 
18 
18 
18 



* The heads of this authority are those due to friction only. 



20 



WESTON ON FLOW OF WATER IN PIPES. 
TABLE No. \— [Continued.) 



No. 



409 
410 
411 
412 
413 
414 



415 
416 
417 



418 
419 
420 
421 



422 



423 
424 
425 
426 
427 



428 
429 
430 
431 
432 
433 
434 
435 
436 



437 
438 
439 
440 
441 
442 
443 
444 
445 
446 



H 



14.76 



16.00 



16.48 



16.99 



19.00 



19.69 



20. CO 



3.92 

8.55 

9.55 

12.72 

18.93 

24.39 



230.00 
420.00 
184.00 



15.09 
43.65 
51 69 
52.39 



303.60 



24.00 
27.50 
34.00 
41.00 
43.50 



* 

0.15 
0.15 
0-20 
0.39 
0.41 
0.69 
0.76 
0.85 
0.82 



719.90 
712.40 
710.70 
705.00 
695.60 
684.40 



25765.00 

29580.00 

3815.00 



25414.00 
31719.00 
31719.00 
26862.00 



4438.70 



22444.00 



328.09 



8171.00 



G o 



4.40 
6.86 
7.33 
8.52 
10.75 
12.30 



5.25 

6.82 

14.51 



1.58 
2.48 
2.71 
3.09 



20.13 



2.06 
2.26 
2.52 
2.73 
2.80 



1.38 
1.47 
1.55. 
2.60 
2.60 
3.42 
3.64 
3.66 
3.69 



0.95 
1.49 
1.93 
2.33 
2-60 
2.87 
3.27 
3.44 
3.74 
3.92 



o 



0.505 



0.182 



0.505 



c 



0.0205 
0.0184 
0.0180 
0.0179 
0.0169 
0.0168 



0.0277 
0.0261 
0.0191 



0.0210 
0.0197 
0.0196 
0.0180 



0.0150 



0.0257 
0.0244 
0.0242 
0.0248 
0.0251 



0.0252 
0.0222 
0.0263 
0.0189 
0.0195 
0.0190 
0.01b3 
0.0205 
0.0194 



0.0271 
0.0214 
0.0210 
0.0205 
0.0213 
0.0206 
0.0200 
0.0207 
0.0209 
0.0210 



Name of the Experimenter, 
etc., and Nature of the 
Pipe. 



Smith. 



Riveted sheet-iron pipe, 
coated with coal-tar and 
asphaltum 



EDINBURGH "WATER Co. 

Cast-iron pipe, in service 
8 or 9 years 



Lampe. 



! New cast-iron pipe, coat- 
[ ed with varnish 

Smith. 

Riveted sheet-iron pipe, 
coated with coal-tar, etc. 

Simpson. 



[ Cast-iron pipe, in service 
f less than thirteen years. 



Dabct. 



► New cast-iron pipe. 



Fanning. 



. Wrought-iron cement 
lined pipe 



* The heads of this authority are those due to friction only. 



WESTON" ON" FLOW OF WATER IN" PIPES. 
TABLE No. 1— {Continued.) • 



21 



<0& 

as 



20.00 



20.00 



20.00 



20.00 



30.00 



30.00 



fr 



w 



0.729 
0.876 
1.029 
1.186 
1.337 
1.490 
1.645 
1.797 



28.13 



16.75 
19.64 
22.52 
25.42 
28.31 
31.19 
34.08 
36.96 
39.84 



* 

1.55 
1.83 
2.11 
2.40 
2.68 

6.27 
7.57 
8.87 
10.17 
11.44 
12.77 
14.07 
15.37 
16.67 
17.96 
19.26 
20.56 
21.86 



8171.00 



1000.00 



29715.00 



4320.00 



fl o 

•rH O 






4.00 
4.04 



2.00 
2.24 
2.36 
2.52 
2.68 
2.76 
2.92 
3.00 



1.44 



2.71 
3.01 
3.31 
3.61 
3.91 
4.21 
4.51 
4.81 
6.11 



•3* 



4120.00 


1.77 


0.505 


4000.00 


1.60 
1.74 




a 


1.87 




<< 

<< 


2.00 
2.14 




J0200.00 


1.47 




ft 


1.62 




it 


1.76 




it 


1.91 
2.06 




«« 

C( 
fC 


2.20 
2.35 
2.50 
2.64 
2.79 
2.94 
3.08 
3.23 






0.505 



t 



0.0210 
0.0211 



0.0197 
0.0188 
0.0198 
0.0200 
0.0199 
0.0210 
0.0206 
0-0214 



0.0491 



0.0568 
0.0539 
0.0508 
0.0482 
0.0459 
0.0437 
0.0413 
0.0394 
0.0376 



0.0237 



00242 
0242 
0.0241 
0.0240 
0.0236 

0.0230 
0.0228 
0.0224 
0.0221 
0.0214 
0.0209 
0.0201 
0.0185 
0.0189 
0.0181 
0.0176 
0.0172 
0.0166 



Name of the Experimenter, 
etc., and Nature of the 
Pipe. 



Fanning. 

Wrought-iron cement 
lined pipe 



Bbush. 



Cast-iron pipe, coated 

Y with tar, in service five 

years 



Bailey. 



Cast-iron pipe, tubercu- 
lated, in service two 
years 



Dakrach. 



Cast-iron pipe, in service 



eleven years. 



Simpson. 

Cast-iron pipe, in service 
two or three years 



Dakrach. 

I New cast-iron pipe. The 
head due to friction, 
does not include the re- 
sistance of two check 
valves which were on 

) this pipe 



Cast-iron pipe, in service 
two years. The head 
due to friction, does 
not include the resist- 
ance of four check 
valves which were on 
this pipe 



20 
20 



20 
20 
20 
20 
20 
20 
20 
20 



26 



26 
26 
26 
26 
26 
26 
26 
26 
26 



21 



21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 



* The heads of this authority are those due to friction only. 



22 



WESTON" ON FLOW OF WATER IN" PIPES. 
TABLE No. 1— {Continued.) 



No, 



497 
498 
499 
500 
501 
502 
503 
504 
505 
506 
507 
508 
509 
510 
511 
512 



513 
514 
515 
516 



517 



518 
519 
520 



2-^ 
ft 



30.00 



486 
487 
488 
489 
490 
491 
492 
493 
494 
495 



496 36.00 



36.00 



48.00 



48.00 



90.00 



PI o 



4."04 
4.62 
5.20 
5.78 
6.35 
6.93 
7.51 
8.09 
8.66 
9.24 



20.22 



3.45 

4.03 

4.61 

5.19 

5.77 

6 35 

13.00 

13.28 

13.57 

13.86 

14.15 

14.44 

14.73 

15.01 

15.30 

15.59 



0.56 
1.24 
2.13 
3.23 



5.00 



* 

3.68 
3.98 
4.17 



4400.00 



11217.00 



3700.00 



12400.00 



1747.20 



5280.00 



7166.00 



1.07 
1.21 
1.34 
1.48 
1.61 
1.75 
1.88 
2.02 
2.15 
2.29 



3.00 



.58 

.74 

.89 

.05 

.21 

.37 

.00 

.11 

.22 

.33 

1.44 

1.56 

1.67 

1.78 

1.89 

2.00 



2.62 
3.74 
4.97 
6.20 



3.46 



3.77 
3.80 
3.93 



® a 
o 



0.505 



c 



0.1283 
0.1160 
0.1053 
0.0966 
0.0892 
0828 
0.0772 
0.0724 
0.0681 
0.0644 



0.0383 



0.0716 
0.0687 
0.0669 
0.0640 
0.0614 
0.0586 
0.2013 
0.1668 
0.1402 
0.1208 
0.1050 
0.0926 
0.0822 
0.0739 
0.0667 
0.0604 



0.0120 
0.0131 
0.0128 
0.0124 



0.0204 



0.0174 
0.0186 
0.0182 



Name of the Experimenter, 
etc., and Nature of the 
Pipe. 



Daeraoh. 



Cast-iron pipe, in service 
nine years 



Greene. 

Cast-iron pipe, 
tuberculated .. 



heavily 



Darrach. 



! Cast-iron pipe, in service 
{ seven years 



I Cast-iron pipe, in service 



seven years. 



Stearns. 

j Cast-iron pipe, coated 
y with coal-tar, in service 
{ three years 



Gale. 



Cast-iron pipe, coated with 
coal-tar, in service eight 
years 



Clarke. 



Brick tunnel , 



2S 



28 
28 
28 
28 
28 
28 
28 
28 
28 

2a 

28 
2S 
28 
28 
28 
28 



21 
21 
21 



21 



22 
22 
22 



* The heads of this authority are those due to friction only. 



WESTON ON" FLOW OF WATER IN PIPES. 23 

DESCEIPTION OF THE EXPERIMENTS THE RESULTS OF 
WHICH ARE CONTAINED IN TABLE NO. 1. 

All of the experiments that were made under the direction of one 
authority are described together, and each description is preceded by 
the title of the work or publication, from which the information upon 
which it is based, was obtained. 

Experiments of Bossut. 

'* Traiie theorique et experimental d'Hydro-dynamique," by the Abbe 

Bossut, Paris, 1786. 

The twenty-nine experiments were made under the direction of the 
Abbe Bossut, an eminent French geometer, Professor of Mathematics 
in the School of Engineers at Mezieres, and Member of the Academy 
of Sciences, with lead pipes, 1.07, 1.42 and 2.14 inches in diameter, 
which in all cases discharged into the open air. Their tabular numbers 
are, 1.07 inch, 104 to 105; 1.42 inch, 146 to 160 inclusive; 2.14 inch, 
238 to 249 inclusive. 

Those numbered in Table No. 1, 104 and 105, 146 to 157, and 238 to 
249 inclusive, were included in the fifty-one experiments that were used 
by Prony in determining his formula, and were made with straight 
pipes. These pipes were supplied with water from a closed metal box 
1 foot square, that was connected by a pipe about 8 inches in diameter 
with a supply reservoir, in which the water was maintained at a con- 
stant elevation. 

The other experiments that were made by M. Bossut, which are 
numbered in Table No. 1, 158 to 160 inclusive, were made with a pipe 
1.42 inches in diameter that was laid on an incline of 6° 30'. The 
upper end of the pipe was connected with a supply reservoir, in which 
the water was kept at a constant head of about 0.89 feet above the 
center of the inlet end of the pips; this head being equivalent to 
the head due to the velocity, and the loss arising from contraction at 
the inlet of the pipe. Three separate lengths of pipe were used in 
making these experiments, the inclination being the same in each 
instance. 

Experiments of Bailey. 

" The Brooklyn Water Works and Sewers," by James P. Kirkwood. 

New York, 1867. 

This experiment was made by George H. Bailey, C. E., with a com- 
pound cast-iron main 29 715 feet long, belonging to the Jersey City 
Water Works. Its tabular number is 457. 

"This main was 20 inches in diameter for a length of 29 587 feet, 
and 24 inches in diameter for a length of 128 feet. It connected the 



24 W£STON ON FLOW OF WATER IN PIPES. 

receiving with the distributing reservoir, and at the time the experi- 
ment was made is said to have been from one to two years old. The 
head was ascertained by leveling between the reservoir surfaces, and the 
flow was measured by the lowering of the surface of the water in the 
feeding reservoir. 

Six experiments were really made, but their average only, as pub- 
lished by Mr. Kirkwood, is given in Table No. 1, and the diameter was 
used by the writer as 20 inches for the entire length of the pipe, in 
computing the co-efficient of friction £. 

Experiments of Brush. 

" Transactions of the American Society of Civil Engineers" Vol. XIX, 

1888. 

The eight experiments were made under the direction of Charles B. 
Brush, M. Am. Soc. 0. E., with a cast-iron pumping main, 20 inches in 
diameter and 75 000 feet long, belonging to the Hackensack Water Com- 
pany. Their tabular numbers are 449 to 456 inclusive. 

This main was laid along by the side of railroads, and in highways, 
with a large number of summits, angles and curves. Among the hori- 
zontal bends there were four right angles and ten quadrants of about 
30 feet radius. It had been in service about five years when the experi- 
ments were made, and there was not any oxidization upon the interior 
surface. The pipes, when new, were coated in the usual way with tar. 
A pressure gauge was used in determining the head. The flow of water 
was measured by the displacement of the pump plungers of a Worth- 
ington pumping engine, 5 per cent, having been allowed for slip. The 
average delivery of the main was about 4 000 000 gallons per day, but 
200 000 of this amount was supplied from the main to consumers, before 
the balance reached the reservoir, 100 000 gallons being taken at a point 
13 500 feet from the pumping station, and the remaining 100 000 at a 
point 70 000 feet from the pumping station. The "effective" head 
ranged from 55 to 135 feet according to the quantity of water flowing 
in the main. The head given in Table No. 1 is the frictional head per 
1 000 feet as given by Mr. Brush. 

Bonn Water Works Experiments. 

"Hydraulics," by Hamilton Smith, Jr., M. Am. Soc. C. E. New York, 

1886. 

The experiments were made with a new cast-iron force main, coated 
with asphaltum, 12.48 inches in diameter and 17 684 feet long, belonging 
to the Bonn Water Works. Their tabular numbers are 397 to 404 in- 
clusive. 



WESTON" ON FLOW OF WATER IN PIPES. 25 

The pipe was "supplied by pumps at the lower end;" it had "no 
obstructions of consequence, such as valves or sharp bends." The dis- 
charge "was determined by absolute measurement in a reservoir, and 
also by capacity of the plungers of the pumps; the two measurements 
agreed closely. Owing to the disturbed condition of the surface of the 
water in the reservoir " the quantity "was probably not very accurately 
determined. The head was determined by manometers at the pumps 
(probably Bourdon gauges attached to the air-chambers of the two 
pumps). There was a small amount of air in the pipe, which may have 
affected accuracy of results." 

Experiments of Couplet. 

" Recherches sur le Mouvenzent des Eaux," by 31. Couplet, Memoirs of the 

Academy of Sciences, 1732. 

Of the fifteen experiments that were made at Versailles under the 
direction of M. Couplet, the writer has selected only six of the seven 
that were included in the fifty-one experiments that were used by Prony 
in determining his formula. The six experiments were made with a 
pipe 5.33 inches in diameter and 7481.7 feet long; for a distance of about 
320 feet the pipe was of stone-ware, and for the remaining distance of 
lead. Their tabular numbers are 309 to 314 inclusive. 

There were several slight turns, and one quite abrupt one, in the 
pipe. The difference between the elevation of the supply tank and the 
vertical outlet of the pipe was ascertained by connecting a temporary 
vertical pipe to the outlet, and allowing the quiescent water to take its 
hydrostatic level. The flow was determined by dividing the discharging 
jet of water into two parts, and measuring each one separately in a vessel 
having a capacity of about 0.63 cubic feet. 

Experiments of Clarke. 

" Main Drainage Works of the City of Boston," by Eliot C. Clarke, M. Am. 
Soc. C. E. Third Edition, 1888. 

The experiments were made under the direction of Mr. Clarke, with 
the Main Drainage Tunnel belonging to the City of Boston, which 
extends under the harbor from the mainland at Dorchester to Squantum 
Neck. Mr. Clarke mentions seven experiments, but the writer has 
selected only the three during which the flow seems to have been deter- 
mined with accuracy. Their tabular numbers are 518 to 520 inclusive. 

The tunnel is circular in form, 90 inches in diameter, 7 166 feet long, 
and lined with hard brick. Jt is flushed once in about two weeks with 
clean salt water, by utilizing the entire pumping capacity of the engines. 
At the time the experiments were made the tunnel was flowing full, and 
the volume consisted of about three-fourths salt water and one-fourth 
sewage. 



26 WESTOK O^T FLOW OF WATER IN" PIPES. 

The flow through the tunnel is generated by the difference in level of 
the elevation of the water at its two extremities. This difference, which 
is the frictional resistance, was carefully ascertained by knife-edged 
sliding gauges. The head was taken a short distance below the entrance 
of the tunnel during the three experiments, in order to avoid a correction 
for entrance. The flow was measured during Experiment No. 520, by the 
displacement of the pump plungers of the pumping'engines, allowance 
having been made for a slip, which was ascertained by trial previous 
to the experiment in the reservoir, in which the flow during Experiments 
Nos. 518 and 519 were measured. 

The section of the tunnel at its farther end increases gradually, 
similar to a diverging tube, which somewhat reduces the resistance, 
while on the other hand, the tunnel has a quarter turn of 9.75 feet 
radius and one angle of 23° 15', which slightly increases the resistance. 

EXPEEIMENTS OF DAECY. 

" Recherches experimentales relatives au mouvement de VEau dans les 
Tuyaux," by Henry Darcy, Paris, 1857. 

The experiments were made under the direction of Henry Darcy, 
an eminent French Civil Engineer, while he had charge of the water 
service of the City of Paris, during the years 1849, 1850 and 1851. 
They will be described at a considerable length, on account of the com- 
pleteness of the apparatus that was used, and the thorough and elabor- 
ate manner in which they were conducted. 

The synoptic table on page 27 gives the nomenclature, etc., of the 
different kinds of pipes that were used in making the 203 experiments. 

At Chaillot, where the experiments were made, the natural facilities 
were very favorable. In a northerly direction from the building con- 
taining the pumping machinery, which was located on the north bank 
of the Seine, there was a circular sheet-iron tank, having a capacity of 
105 677 gallons, elevated about 134.50 feet above the ground where the 
experimental plant was set up. In the same direction there were also four 
large reservoirs of different elevations, which could be connected with, 
each other or isolated at will, each having a capacity of 873 589 gallons; 
their respective elevations were 77.10 feet, 81.70 feet, 83.99 feet, and 
86.95 feet. 

The circular tank was supplied by the pumping machinery through 
a conduit 9. 84 inches in diameter, and the four reservoirs were supplied 
from the same source through a conduit 25.59 inches in diameter. 

In the rear of the building containing the pumping machinery there 
was a cistern, suitable for measuring large quantities of water, which 
was ordinarily used to receive condensation water. 



WESTON" ON FLOW OF WATER IN PIPES. 



27 



<s> . 

P< <0 

WO 
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o 

go 

S a 

ga 

a 



13 

17 

12 

7 

7 

7 

12 

12 

11 

7 

6 

13 

10 

9 

9 

14 

13 
16 



0.480 
1.047 
1.550 
0.551 
1.063 
1.610 
1.055 

3.25 

7.72 
11.22 
1.96 
3.22 
5.39 
7.40 
19.69 

1.43 

3.15 

9.63 
11.69 



Nature of the Pipes. 



New wrought- iron pipe 

New lead pipe 

it ft 

New sheet-iron pipe, coated ) 
with bitumen. I 

€t CI 

New glass pipe 

New cast-iron pipe 

it i < 

(Old cast-iron pipe, lined with) 
{ deposit, and the same cleaned ] ' ' 

n it 

Old cast-iron pipe.thoroughly cleaned. 



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Em 




on 

a 

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O 


a 


.a . 


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°"K 






03 £ 


A 


to 


«wfe 




a 

CD 

Hi 




o 


Is 

o 
H 


a 

03 
Hi 


a 

es 


374.61 


7.05 


Screw.. 


372.23 


8.10 


" 


371.92 


12.63 


" 


172.05 


38.55 


Solder. 


172.38 


21.65 


" 


172 41 


17.06 


" 


371.86 


9.15 


Screw.. 


365.07 


9 51 


" 


365 32 


9.51 


" 


365.47 


9.51 


" 


184.56 


3.81 


Flange. 


366.10 


8.20 


Socket. 


365 74 


8.20 


«« 


365.40 


8.20 


" 


365.34 


8.20 


" 


374.94 


4.27 


Flange. 


366.31 


8.20 


Socket. 


365.35 


8.20 


Flange. 


365.28 


8.20 


Socket. 



» • 

t-> o 

a-2 



15 to 27 
61 to 77 

212 to 223 
34 to 40 
97 to 103 

224 to 230 

85 to 96 

296 to 307 
338 to 348 
370 to 376 
231 to 236 
283 to 295 
315 to 324 
329 to 337 
428 to 436 

161 to 174 

270 to 232 
349 to 364 
377 to 384 



The water used in making the experiments was taken from the 25.59 
and 9.84-inch conduits, at a point about 325 feet north of the pump 
building. A vertical pipe of the same diameter as the conduit, and of 
suitable length, was connected to the 25.59-inch conduit; there was con- 
nected at a right angle, to the upper part of this vertical pipe, a conduit 
11.81 inches in diameter; upon the 11.81-inch conduit there was a 
gate about 3 feet from the vertical pipe; two lead pipes 0.55 and 1.61 
inches in diameter were arranged as connections between the vertical 
pipe and the 11.81-inch conduit, beyond the gate. The 9.84-inch con- 
duit was also connected with the 11.81-inch conduit, beyond the gate, 
by a lead pipe 1.06 inches in diameter. Each of these small pipes was 
supplied with a stop-cock. 

When the four large reservoirs were used, and small volumes required, 
the water was taken through the 0.55-inch pipe, its stop-cock having 
been opened more or less, dependent upon the requirements of the 
experiments; if the flow was not sufficient through this pipe it was shut 
off and the 1.61-inch pipe brought into service, which in due course was 
abandoned for the 11.81-inch conduit. 

In this manner all the heads were utilized that could be furnished by 
the reservoir having the lowest elevation, which was maintained at a 
constant level by means of the water that was contained in the three 
others more elevated. 



28 WESTON ON FLOW OF WATER IN PIPES. 

To obtain greater heads, communication was established with the 
sheet-iron circular tank, by opening the stop-cock on the 1.06-inch pipe, 
through which the water passed from the 9.84-inch conduit, which was 
supplied by this tank. 

About 48 feet beyond the gate the 11.81-inch conduit was connected 
with a horizontal cast-iron cylinder 11.50 feet long ; and 3.28 feet in 
diameter. 

The horizontal cylinder formed an intermediate reservoir, and was 
intended to deaden the velocity of the water before it entered the expe- 
rimental conduits. In the interior there was a vertical sheet-iron dia- 
phragm perforated with holes, through which the water passed after its 
entrance from the 11.81-inch conduit. One end of the cylinder consisted 
of a semi-circular cap, and the other of a vertical plate to which the 
experimental conduits were connected. 

The conduits used in making the experiments were laid upon blocks 
of masonry, on an incline inverse to the flow, in order to more easily free 
them from air. 

The outlet end of each conduit discharged under water and was con- 
nected to the lower part of one of two vertical cast-iron cylinders. The 
bottoms of the cylinders were closed and the tops open. Each conduit 
had a gate or stop-cock located upon it at a short distance from where it 
entered its respective cylinder. These outlet cylinders were not of the 
same size, the larger was 5.30 feet in diameter and 10.93 feet high, and 
the smaller was 1.05 feet in diameter and 6.56 feet high. Only one of 
them was used at one time, the size depending upon the diameter of the 
conduit being experimented upon, and the volume of water flowing. A 
double communication was established between the large cylinder and 
the gauging basins; one of these communications was composed of a 
pipe 4 inches in diameter, which served to carry the water to a small 
gauging basin when small volumes were used; the other consisted of a 
notch 2.62 feet wide and 1 foot deep, at the top of the cylinder, into 
which was fitted a wooden channel which carried the water to the large 
gauging basins in the rear of the pump building; the 4-inch pipe was con- 
nected at a lower elevation than the channel, and when the capacity of 
the small gauging basin was insufficient, the inlet was stopped with a 
wooden plug, and the water rose in the cylinder and escaped by the 
channel. The water which entered the small cylinder was conducted to 
one of three small gauging basins, dependent upon the volume of water 
flowing, by means of a pipe 3.19 inches in diameter; this pipe had a 
movable elbow by which the water could be directed into either of the 
three, at will. 

Seven gauging basins could be employed for measuring the water 
discharged by the experimental conduits. In order to be described 
more clearly, these basins will be numbered 1, 2, 3, 4, 5, 6 and 7. Basins 
Nos. 1, 2, 3 and 4 were formed by masonry division walls, which were 



WESTON ON FLOW OF WATEK IN PIPES. 29 

located in the large rectangular cistern in the rear of the pump building; 
one wall divided the cistern into two equal parts, and another subdivided 
the one of these parts nearest to the pump building; by this arrange- 
ment there were available three basins, Nos. 1 and 2 each having an 
area about one-fourth of the total area of the cistern, and No. 3 having 
an area about one-half of the total area of the cistern; the wooden channel 
emptied into No. 1, which was located nearest to the vertical outlet 
cylinders; No. 4 was composed of the upper part "of the cistern, from 
the level of the summit of the dividing walls to a point about 8.20 feet 
above these walls. 

Two float gauges, located in Nos. 1 and 3, were used to measure 
the height of the water. Basins Nos. 1, 2 and 3 drained into the Seine, 
and could be connected or isolated at will; measurements were not 
made in Nos. 1, 2 and 3 until the water had covered their inverts, and 
not in No. 4, which was used only in making experiments with conduits 
of the largest diameter, until the water had reached a level above the 
division walls. Great care was taken in ascertaining the capacity of 
these basins, and in determining the amount of water that was lost by 
filtration and leakage from them; the amount lost in this way, however, 
was generally very insignificant. 

The small gauging basins Nos. 5, 6 and 7, which were located quite 
near the outlet cylinders, were vertical cylinders with open tops; Nos. 
5 and 6 were made of cast-iron, and No. 7 of lead; they all had stop- 
cocks or plugs, conveniently arranged for letting out the water after each 
experiment. On the outside of each there was adjusted a glass tube, 
which was connected with the interior, for measuring the elevation of 
the water, which was accomplished by placing a scale about 6.50 feet 
long against the tubes. Their respective diameters and heights were as 
follows : 

Diameter. Height. 

No. 5 3.15 feet 7.45 feet. 

No. 6 1.08 " 8.20 " 

No. 7 0.33 " 8.20 " 

Five water and five mercurial manometers were used to determine 
the heads, and each set, to facilitate description, will be numbered 1, 2, 
3, 4 and 5. (In reality, however, there were but four different mano- 
metric tubes, etc., as Nos. 3 and 4 consisted of one tube, etc., which 
was connected to the experimental conduits at two different points.) 
They were all set up against one post, which was located about half way 
between the horizontal inlet and vertical outlet cylinders, in order to be 
able to compare their indicated results without a possibility of error. 
The manometers were connected at different points to the experimental 
conduits, and to the horizontal cylinder, by lead pipes 0.55 inches 
in diameter, which were laid upon planks placed upon the masonry 
blocks that support the experimental conduits. A ladder was erected 
by the side of the post for convenience in observing the manometers. 



30 WESTON ON FLOW OF WATER IK PIPES. 

Small closed reservoirs of a capacity of about 0.6 of a cubic foot were 
established upou the 0.55 inch manometer pipes near their junctions 
with the experimental conduits, with the exception of the pipe connect- 
ing manometer No. 5, the reservoir of which was located near the foot 
of the manometer post; in the upper part of these reservoirs, as well as 
at the highest points of the 0.55-inch pipes, the experimental conduits, 
the manometers, and the horizontal cylinder, air vents were established. 

Water manometers were employed for all heads that did not exceed 
19.69 feet, and mercurial manometers for heads above 19.69 feet. 

The water manometers were adjusted upon a vertical plank graduated 
to millimeters, which was fastened to the front of the post facing the 
experimental conduits. 

Each water manometer consisted of a vertical glass tube about 18 feet 
in length, formed by joining together in a copper fitting, with gum-lac, 
two glass tubes about 9 feet in length. They were all operated in the 
same manner, and had stop cocks at their junctions with the 0.55 inch 
connecting pipes. 

The mercurial manometers were adjusted upon two vertical planks 
graduated to millimeters, which were erected behind the post; they were 
connected to the same 0.55 inch lead pipes that served as connections 
between the water manometers and the experimental conduits; and stop- 
cocks were so arranged that either the water or the mercurial mano- 
meters could be used at will. 

Each mercurial manometer consisted of the following combination. A 
straight lead pipe rose to a height of about 6.30 feet above the bottom of 
the graduated plank; one end of a copper tube, about 4 inches long, was 
connected at a right angle with the upper end of the lead pipe by an 
elbow; a glass tube of the same length as the lead pipe was connected at 
a right angle with the other end of the copper tube by an elbow, and ran 
down in a direction parallel to the lead pipe to the bottom of the plank; 
one end of an iron tube, about 4 inches long, was connected at a right 
angle with the lower end of the glass tube; a second glass tube about 9 
feet in length was connected at a right angle with the other end of the 
iron tube, by an elbow, and ran up parallel to the other glass tube and 
the lead pipe to the top of the plank. The iron tube had connected to 
its lower side a rubber pocket, containing mercury, which was intro- 
duced by pressure into the two glass tubes ; this pocket, which had a 
stop-cock upon its connection with the iron tube, also served to receive 
the mercury when it was necessary to discharge the manometer. The 
copper tube had a stop cock connected to its upper side over the shorter 
glass tube, to allow the introduction of a w T ire when it was necessary to 
free the tube of air. The joints of the lead pipe and glass and metal 
tubes were made respectively of solder and gum-lac. 

Manometer No. 5 was connected to the horizontal cylinder, or inter- 
mediate reservoir, near its outlet end. Manometer No. 4 was connected 



WESTON" ON FLOW OF WATER IN PIPES. 31 

to the experimental conduits quite near the horizontal cylinder. The 
difference between the readings of manometers Nos. 5 and 4, when small 
conduits were being used, gave the approximate loss of head due to the 
entrance of the water into the conduits from the horizontal cylinder, 
plus the head due to the velocity in the conduits. Manometer No. 3 
was connected to the lead conduits 7.09 feet from the horizontal cylinder, 
and to the other conduits (with the exception of those of glass, the dis- 
tance for which is not given by Mr. Darcy), from 13.68 to 19.29 feet from 
the horizontal? cylinder. By an arrangement of cocks and connections, 
one 0.55 inch lead connection pipe served for both manometers Nos. 3 
and 4. Manometer No. 2 was connected to all of the experimental con- 
duits 164.05 feet from No. 3, with the exception of those of lead and 
glass, which were connected, respectively, 82.03 and 76.41 feet from No. 3. 
Manometer No. 1 was connected to all of the experimental conduits 
164.05 feet from No. 2, with the exception of those of lead and glass, 
which were connected, respectively, 82.03 and 69. 79 feet from No. 2. The 
distance from manometer No. 1 to the vertical outlet cylinders was upon 
the lead conduits about 16.41 feet, and upon the others, with the excep- 
tion of the glass conduit, from 14.60 to 19.85 feet. 

At first sight manometer No. 2 might not seem necessary, but it ren- 
dered great service during the experiments as a check upon Nos. 1 and 
3, as well as in detecting, on several occasions, disturbances which would 
have materially interfered with the experiments, and which probably 
would not have been known but for this supplementary manometer. 
For instance, all things being equal, the difference in the observations of 
manometers Nos. 1 and 2 should be the same as the difference in the 
observation of Manometers Nos. 2 and 3. In actual practice, however, 
they were never exactly the same, as a slight variation in the mean 
diameter of the conduit, between either of these points, would cause a 
slight difference ; but under these circumstances, as the difference was 
always in the same sense for all heads, the reason was readily under- 
stood. When these conditions were not fulfilled it was generally owing 
to leaks or accumulations of air. 

There was also placed against the large outlet cylinder a graduated 
board with two glass tubes; one of these tubes was connected with the 
interior of the cylinder, and indicated the height of the water that it 
contained, and the other was connected to the experimental conduit 
near the cylinder, and indicated the head of the water moving in the 
conduit. 

In all computations, the difference in the heights indicated by man- 
ometers Nos. 1 and 3, were always taken as the losses of head, and the 
lengths used were the distances between the points where these 
manometers were connected to the experimental conduits. The dis- 
tance between Nos. 1 and 3 was for the glass conduit, 147.19 feet; for 
the lead conduits, 164.05 feet, and for all the other kinds of conduits, 



32 WESTON ON FLOW OP WATER IN PIPES. 

328.09 feet. As the manometers were connected at the joints of the 
glass conduit, it was not possible to make the distances between Nos. 1 
and 2 and Nos. 2 and 3 the same. 

The absolute heads of the large reservoirs at Ohaillot, or the circular 
sheet-iron tank, were used during the greater portion of the experi- 
ments. In order to vary the head for each experiment, while experi- 
mental conduits of large diameter were being used, the gate, or the stop 
cock of the branch conduits through which the water flowed that 
supplied the horizontal cylinder at the time, was throttled. This could 
not be done satisfactorily, however, when experiments were being 
made with small conduits. Two new apparatus were therefore con- 
structed, for making the experiments with the glass and lead conduits, 
and with the wrought iron conduits 0.48 and 1.047 inches in diameter, 
by means of which reservoirs were formed of constant elevation, which 
furnished the different heads that were required. 

The apparatus which was used with the wrought-iron experimental 
conduits consisted of a cast-iron column, composed of flanged pipes 
9.84 inches in diameter. A lead pipe 0.55 inches in diameter, which 
was run up the side of the column and bent over the top, supplied 
the water while the experiments were being made; in the lower part 
of this lead pipe a cock served to shut off the water entirely, or to mod- 
erate the flow; the supply could also be regulated by means of a cock 
in the horizontal cylinder, to a branch of which the other end of the pipe 
was connected. Another lead pipe, 1. 06 inches in diameter, was connected 
to a small branch at the bottom of the column, and ran up verti- 
cally by the side of the column; in this lead pipe, at convenient dis- 
tances apart, there were branch openings, which were stopped with 
wooden plugs. A ladder was erected by the side of the column in order 
to manouver the plugs. When it was necessary to operate with the 
least head, the lower plug was removed, and by means of the cock in 
the lower part of the lead supply pipe, the arrival of the water was 
regulated in such a manner as to allow but a very small quantity to 
escape by the branch opening from which the plug had been removed, 
thereby maintaining a supply of water in the column at a constant level. 
In order to maintain a higher head, one of the upper plugs was removed 
and all the lower openings closed. The greatest head was obtained by 
closing all the branch openings and letting the water flow over the top 
of the column. The experimental conduits for which this apparatus 
was constructed, were connected to the lower part of the column and 
had a regulator cock near their origin. Manometer No. 5 was connected 
to the same branch as the 1.06-inch vertical lead pipe with the different 
branch openings. 

The other apparatus, which was used with the lead and glass con- 
duits, was constructed by taking the horizontal cylinder, 3. 28 feet in 
diameter, and placing it vertically upon its semi-circular end, and con- 



WESTON ON FLOW OF WATEE IN PIPES. 33 

necting vertically to its other end a portion of the 9.84 inches cast-iron 
column that was used in making the experiments with the wrought-iron 
conduits. In order to create at will reservoirs of different levels, a suffi- 
cient length of the lead pipe with branch openings that had previously 
been connected to the cast iron column was connected to a branch at 
the lower end of the cylinder. Manometer No. 5 was connected to the 
same branch as the vertical lead pipe with branch openings. The 
supply of water was brought from the large conduits that formerly 
supplied the horizontal cylinder, by a lead pipe 1.61 inches in diam- 
eter, which was connected to a branch on the side of the cylinder 
opposite to the branch where manometer No. 5 and the vertical lead 
pipe with branch openings were connected; there was a stop cock on 
this supply pipe near its connection with the cylinder, to regulate the 
flow of water. The experimental conduits for which this apparatus 
was constructed were connected to a branch in the front of the cylinder, 
which was situated about half way between the branches where the 
supply pipe and vertical lead pipe were connected. Each experimental 
conduit had a stop cock near its junction with the cylinder to shut off 
the supply of water when necessary. 

The experimental conduits of wrought-iron, lead and glass, for which 
the two apparatus that have just been described were constructed, dis- 
charged into the smallest of the two vertical outlet cylinders, and the 
general arrangement of the stop-cocks and manometers upon these con- 
duits, with the exception of manometer No. 5, was the same as upon the 
other conduits. 

General Observations Relating to Darcy's Experiments. 

The pipes of each diameter were forced as close together as possible, 
in order to prevent the joints from interfering with the flow of the water. 

Before commencing the experiments, the conduits were always tested 
under pressure, and if any leaks were discovered they were immediately 
repaired, even though they were of the most minute description. 

After the conduits were in position the manometers were connected,, 
and the locations of Nos. 1, 2 and 3 were determined with much care. 
After having connected manometer No. 2 at a convenient point near the 
manometer post, the proper distances were measured off above and 
below manometer No. 2, for fixing the positions of manometers Nos. 1 
and 3. The measurements were made with an iron rod 16.41 feet in 
length. 

Upon the cast-iron conduits 3. 15 inches in diameter and above, the 
taps or stop-cocks of the 0.55-inch manometer connecting pipes were 
screwed into the cast-iron at right angles to the center of the conduits. 
These stop-cocks were filed at their lower ends to conform to the curva- 
ture of the interior of the conduits, beyond the surface of which they 
were not allowed to project. 



34 WESTON ON FLOW OF WATER IN PIPES. 

Upon the conduits less than 3.15 inches in diameter, and upon the 
sheet-iron conduits coated with bitumen, the taps or stop- cocks of the 
manometer connecting pipes were soldered, above a hole from 0.08 to 
0.12 inches in diameter. 

The conduits, the stop- cocks, the joints, the air-cocks or vents, and 
the manometers, were all constantly under the most careful supervision; 
it was frequently necessary, however, notwithstanding the precautions 
taken, to make some of the experiments over a second time, on account 
of a small leak having been discovered at their conclusion, upon some 
portion of the apparatus. 

Before commencing the experiments upon a conduit, the manometers 
were tested, by opening their stop-cocks and air vents, and putting the 
conduits under pressure Much difficulty was always experienced when 
the first experiment was commenced, in freeing the manometer pipes of 
air, and it was frequently necessary to let the water flow a long time 
under the greatest possible head in order to do so. During the experi- 
ments upon the conduit 0.48 inches in diameter, one entire day's work was 
entirely eliminated on this account, the difficulty being finally overcome 
by letting the water flow all night. 

In order to be certain that the manometers were free from air, the 
difference of the readings of manometers Nos. 2 and 3, and Nos. 1 and 2, 
were compared. These differences, as has been previously mentioned, 
should be nearly equal, when the water was flowing in the conduits, if 
the manometers were working properly. Another test with the water 
at rest, was also made at times, during which the readings of all the 
manometers were exactly the same if they were entirely free from air. 

Nearly all of the experiments were commenced with slight heads. 
As soon as the desired head was obtained, pins were put into the 
graduated plank to mark the heights of the manometers, and the water 
was allowed to flow long enough to acquire its normal regimen. When 
the water, or mercury, in the manometers became stationary, proceed- 
ings were taken to measure the discharge of the conduit. 

The same person observed the heights of all the manometers when it 
was possible. While experiments were being made with low heads the 
observer was required to remain upon the manometer ladder the whole 
of the time, in order to have his eyes fixed constantly upon the mano- 
meters, and if a noticeable change in the heights, or an oscillation of 
extraordinary amplitude was observed, the experiment was commenced 
over again. 

It was the duty of the person detailed to observe the heights of the 
manometers to watch carefully the conduits, the manometers and the 
other apparatus, in order to be assured that everything was working 
properly. 

Considerable difficulty was experienced in making the experiments 
with high heads, as it was necessary to use mercurial manometers. Two 



WESTON ON FLOW OF WATER IN PIPES. 35 

consecutive experiments were never made without it being necessary to 
repair one or more joints, and frequently repairs had to be made several 
times during the same experiment. 

In order to verify some of the calculations which necessitated the use 
of the mercurial manometers, the water manometer No. 1 was always 
left open, and No. 2, also, when the heads were not too great. 

Heights of water were thus obtained, with which the heights indi- 
cated by the mercurial manometers could be compared. 

The highest accuracy was always maintained in measuring the dis- 
charge of the conduits, and the same watch graduated to seconds was 
nearly always used. 

The time consumed in making each experiment ranged from 135 to 
3 240 seconds; it was rarely less than 240 seconds, however. 

Extraordinary care was taken in determining the mean diameter of 
the conduits. 

The diameters of the conduits 0.48, 1.05 and 1.56 inches in diameter, 
were ascertained by means of the quantity of water that they were able 
to hold. The water was drawn from a reservoir of well- determined sec- 
tion, that was placed in an elevated position, and under which the con- 
duits were vertically arranged in fractions of length. 

At each operation account was kept of the lowering of the water in 
the reservoir, and the product of the sum of the successive lowerings by 
the section of the reservoir gave a cube, which, divided by the lengths 
of the conduits, gave the mean section, from which was obtained the 
jnean diameter. 

The conduits 0.55, 1.06 and 1.61 inches in diameter, of drawn lead, 
had a diameter perfectly well established. 

The sheet iron conduits, coatel with bitumen of 1.06 and 3.25 inches 
in diameter, and the glass conduit of 1.96 inches in diameter, were 
determined by the first process described. 

When the diameters of certain conduits were too large for the above 
process to be easily carried out, or when it was a question of conduits lined 
with deposit, the diameters were ascertained by means of the total capa- 
cities of the conduits, the latter being in place. This proceeding, which 
was followed in determining the diameters of the sheet-iron conduit 
coated with bitumen, 7.72 inches in diameter, and the cast-iron conduits 
1.43, 3.15 and 9.63 inches in diameter, was carried out in the following 
manner: 

Fii*sl. — The extreme pipe was first dismounted (that is to say, the 
pipe contiguous to the feeding horizontal cylinder at the head of the 
conduit, and towards which the conduit sloped), thus allowing the water 
to flow entirely out of the conduit. 

During this operation the gate at the other extremity of the conduit 
near the vertical outlet cylinder, was kept closed, the cylinder having 
been previously filled with water. 



36 WESTON" OK FLOW OF WATER IK PIPES. 

Second. — The extremity of the conduit which had been disconnected 
from the horizontal feeding cylinder was plugged. At the extremity of 
this plug a curved pipe with a stop-cock was connected, in order to 
allow the air to escape, while the conduit was being filled from the ver- 
tical cylinder by the opening of the gate. 

Care was taken to note the height of the water in the vertical cylinder 
before and after the filling. 

A stop-cock to facilitate the escape of air was placed at the middle of 
the conduit. 

Third. — In order to fill the conduit, the gate near the vertical outlet 
cylinder was opened, and two observers, one of whom was placed at the 
middle of the conduit, and the other at the extremity by the plug, 
closed the air-cocks as soon as the water appeared. The gate was then 
closed, and from the lowering of the water in the vertical cylinder the 
mean section of the conduit was determined, from which was calcu- 
lated the mean diameter. 

The diameters of the sheet-iron conduit coated with bitumen, 11.22 
inches in diameter, and the cast-iron conduits 3.22, 5.39, 7.40, 11.69 and 
19.69 inches in diameter, were obtained by direct measurements. 

The diameters of the conduits lined with deposit, given in Table No. 
1, are the diameters of the conduits after they were cleaned, and not the 
diameters used by Mr. Darcy, which took into consideration the thick- 
ness of the deposit. 

Experiments of Dubuat. 

" Principes d' Hydraulique," by Chevalier Dubuat, Paris, 1786. 

Chevalier Dubuat, who was a celebrated French Civil Engineer, 
made quite a number of experiments with various sizes and lengths of 
pipe. The writer, however, has selected only the eighteen that were 
included in the fifty-one experiments used by Prony in determining his 
formula, which were made with a tin pipe 1.07 inches in diameter. 
Their tabular numbers are 106 to 123 inclusive. 

The pipes used in making the eighteen experiments appear to have 
been laid straight, and discharged sometimes under water, and some- 
times into the open air. 

Experiments of Darrach. 
" Transactions of the American Society of Civil Engineers ," Vol. VII, 1878. 

The fifty-three experiments were made under the direction of C. G. 
Darrach, M. Am. Soc. C, E., with six cast-iron pumping mains, one of 
20, three of 30, and two of 36 inches in diameter, belonging to the 
Philadelphia Water Works. The pipes were coated with coal tar in the 
usual way, before being laid. 

The experiments that were made with each main are described sep- 
arately, and each description is preceded by the tabular numbers of the- 
experiments to which it refers. 



WESTON OK" FLOW OF WATER IN" PIPES. 37 

Pressure gauges were used in determining the head. 

Twenty-inch. — Nos. 458 to 466 inclusive. This main was eleven 
years old when the experiments were made. It had one quarter turn. 
The flow was measured by the displacement of the pump plungers of a 
Worthington pumping engine, 5 per cent, having been deducted for 
slip. The presure gauge was connected with the pump. 

Thirty-inch. — Nos. 473 to 485 inclusive. This main was about two 
years old when the experiments were made. It had four check-valves, 
the weight of which produced a pressure equivalent to 1.8 pounds per 
square inch, for which allowance was made in the frictional head given 
in Table No. 1. The flow was measured by the displacement of the 
pump plungers of a Cramp pumping engine* 5 per cent, having been 
deducted for slip. The pressure gauge was connected with the air 
chamber. 

Thirty-inch. — Nos. 468 to 472 inclusive. This main was laid the 
same year that the experiments were made. It had one quarter turn. 
All the other curves had a radius of 25 feet. It also had two check- 
valves, the weight of which produced a pressure equivalent to 1.3 
pounds per square inch, for which allowance was made in the frictional 
head given in Table No. 1. The flow was measured by the displace- 
ment of the pump plungers of a Worthington pumping engine, 5 per 
cent, having been deducted for slip. 

Thirty -inch. — Nos. 486 to 495 inclusive. This main was about nine 
years old when the experiments were made. It had one curve of 
short radius. The flow was measured by the displacement of the pump 
plungers of a Worthington pumping engine, 5 per cent, having been 
deducted for slip. The pressure gauge was connected with the main 
outside of the check- valve. 

Thirty-six-inch. — Nos. 497 to 502 inclusive. This main was seven 
years old when the experiments were made. All the curves had a radius 
of 25 feet. The flow was measured by the displacement of the pump 
plungers of a Simpson pumping engine. 

Thirty-six-inch. — Nos. 503 to 512 inclusive. This main was seven 
years old when the experiments were made. All the curves had a radius 
of 25 feet, with one exception, when 90 degrees were turned with a 
-["-pipe. The flow was measured by the displacement of the pump 
plungers of a Worthington pumping engine, 5 per cent, having been 
deducted for slip. The pressure gauge was connected with the stand- 
pipe. 

Experiments of the Edinburgh Water Company. 

** Excerpt Minutes of the Proceedings of the Institution of Civil Engineers ," 

Vol. XIV, Session 1854-55. 

The three experiments were mentioned by Mr. James Leslie, M. 
Inst. C. E., in a paper on the flow of water through pipes, conduits, 
etc. Their tabular numbers are 415 to 417 inclusive. 



38 WESTON" ON PLOW OF WATER IN" PIPES. 

They were made with the Clointon cast-iron main between Clubbie- 
Dean Reservoir and Castle Hill. This main was 16 inches in diameter 
and eight or nine years old. 

One experiment was made with the total length of the pipe, 29 580 
feet; one with a length of 25 765 feet, between Torduff Cistern and Castle 
Hill; and one with a length of 3 815 feet, between Clubbie-Dean Reser- 
voir and Torduff Cistern. In the first instance 'fifteen observations 
were made, in the second twenty -five, and in the third one. 

Experiments of Fanning. 

" A Practical Treatise on Hydraulic and Water Supply Engineering :," by 
James T. ^Fanning, C. E. New York, 1882. 

The twelve experiments were made with a wrought-iron cement-lined 
pipe, 20 inches in diameter, and 8 171 feet long. Mr. Fanning does not 
mention the manner in which they were conducted. Their tabular num- 
bers are 437 to 448, inclusive. 

Experiments of Gale. 
" Transactions Institution of Engineers in Scotland" Vol. XII, 1869. 

The experiment was made under the direction of James M. Gale, 
M. Inst. C. E. , with a cast-iron main, 48 inches in diameter, and 5 280 
feet long, that conducted a supply of water from Loch Katrine to the 
City of Glasgow. Its tabular number is 517. 

The writer is indebted to Mr. James Forrest, Secretary of the Insti- 
tution of Civil Engineers, for the following additional information : 
" Mr. Gale informs me that the pipes referred to in his paper had been 
at work for eight years prior to the date of the observations. Beforo 
being laid they were coated by the late Dr. R. A. Smith's patent process, 
and this coating had been very little affected by rust when the observa- 
tions wera made. He has recently seen some of these pipes " (August, 
1884) , ' ' and finds that the tubercles inside are increasing in size and num- 
ber, and he has no doubt that the discharge is falling off. The quantity 
of water delivered was measured over a weir 40 feet wide, in four bays 
of 10 feet wide each. The plates were of cast-iron brought to a thin 
edge. The formula used was cubic feet per minute = 214 A -\/ h. " 

Experiment of Greene. 

" The Brooklyn Water Works and Seivers" by James P. Kirkwood. New 

York. 1867. 

This experiment was made by General George S. Greene, with a cast- 
iron main, 36 inches in diameter, and 11 217 feet long, belonging to the 
Brooklyn Water Works. Its tabular number is 496. 



WESTON ON" FLOW OF WATER IK PIPES. 39 

This main connected the receiving with the distributing reservoir. 
It was heavily tuberculated, and had three-quarter circle curves of 90 
feet radius each. 

The head was ascertained by leveling between the reservoir surfaces, 
and the flow was measured by the lowering of the water in the upper or 
feeding reservoir. 

Experiment of Hodson. 

" Hydraulic Tables, Co-efficients and Formulas ," by John Neville, C. E., 

London, 1860-61. 

Mr. Neville states that the results of this experiment, which was 
made with a pipe 1 inch in diameter and 100 feet long, was given to him 
by Mr. Hodson, of Lincoln. 

As Mr. Neville used 0.352 as the co-efficient of influx in connection 
with this experiment, the writer has done the same. 

Experiments of Jaedine. 
" Brewster's Encyclopaedia." 

The experiment was made with a lead pipe 4£ inches in diameter, and 
14 930 feet long, belonging to the Edinburgh Water Works. Its tabular 
number is 308. 

Mr. Jardine states that the jflow through the pipe was 11-g- cubic feet 
per minute, for the years 1738-42. The velocity given in Table No. 
1 is computed from these data. 

Experiments of Leslie. 

" Excerpt Minutes of Proceedings of the Institution of Civil Engineers" 

Vol. XIV, Session, 1854-55. 

The experiments were made under the direction of James Leslie, M. 
Inst. C. E. 

Mr. Leslie made sixty-four experiments with new lead pipes 2|, If 
and li inches in diameter. The writer has selected, and included in 
Table No. 1, only twenty of the thirty-eight experiments that were made 
with pipes 2^ inches in diameter, ranging in length from 100 to 1 086 feet; 
these experiments were simply selected so as to include velocities from 
0.22 to 6.91 feet per second, the latter velocity being the highest that 
was obtained with these lengths of pipe. Their tabular numbers are 
250 to 269 inclusive. 

The experiments were commenced with a pipe 1 086 feet long; "the 
pipe was afterwards cut, successively, to the lengths of 540, 270, 100, 25 
and 10 feet." 

"The pipe was coiled nearly in a circle of 90 feet in diameter, 
and when of its integral or full length it made four revolutions. 



40 WESTON" ON FLOW OF WATER IN" PIPES. 

Each, upward curve was tapped by a small gimlet hole, into which a 
wooden plug was inserted; these were all taken out frequently to allow 
the air to escape, and were kept out until only water, free from air, 
issued from the orifice. The ends of the pipe, in each case, were 
inserted into the sides of two cisterns, each measuring 2 feet 6 inches by 
1 foot 3 inches, and 2 feet deep, and were about 22 inches below the 
surface of the water. In order to be perfectly assured that there could 
be no mistake in the levels, the two cisterns were placed quite close 
together, and the head was measured by the difference of the respective 
surfaces of the water." The head could be varied at will by raising or 
lowering the upper cistern, which was supplied with water by a pipe 
that was carried up over the top, thence nearly to the bottom of the 
cistern. The water overflowed from the lower or outlet cistern, which 
was fixed, into a measuring box. 

' ' The pipes were carefully joined and soldered, so as to have no internal 
obstruction, with the exception of one joint, where it was discovered, 
that by some accident, a little solder had got inside and caused a slight 
obstruction. The extent of it measured only about one twenty-fifth part 
of the area of the pipe, and would, it is imagined, be so trifling as not 
to appreciably affect the flow." 

Experiments of Lampe. 

" Der Civilingenieur." Vol. XIX, 1873; and "Hydraulics," by Hamilton 
Smith, Jr., M. Am. Soc. C. E. New York, 1886. 

The four experiments were made with a 16-inch main, by Professor 
Dr. C. J. Lampe, an eminent German scientist. Their tabular numbers 
are 418 to 421 inclusive. 

They are described by Mt. Smith as follows: "The pipe experi- 
mented upon was a cast-iron conduit, which conveyed by gravity a 
supply of spring water to the Town of Danzig. . It had a total length of 
46 352 feet; the lower 9 040 feet in length had a considerably steeper 
inclination than the upper portion, so there were two hydraulic grade 
lines; the four experiments, however, were made upon the upper portion 
of the pipe. The pipe was laid in 1869; it had three curves, each of 10.3 
feet radius, and a number of very easy curves as it followed the general 
contour of the ground. The pipe was coated with a patent varnish 
which did not appreciably diminish its section. Examination showed 
that from 1869 to 1871 the character of the inner surface had very slightly 
changed; the only material adhering to the surface in 1871 could be 
readily removed by rubbing with the finger, there being no signs of 
rust. The joints were 12 feet in length, united by lead and hemp pack- 
ings. There were twenty-six air-cocks attached to the pipe along its 
course." 



WESTON ON FLOW OF WATER IN PIPES. 41 

"The mean velocity was ascertained by measuring the discharge 
* * * in a masonry reservoir situated at the outlet end of the pipe. 

"The pressures were determined by connecting a quicksilver mano- 
meter, first with one of the air-cocks, and then with another ; these 
pressure determinations were not synchronous with the measurement; 
but, in some instances, several days apart. As in none of the four ex- 
periments was the pipe filled at its inlet, this lack of synchronism 
appears to form a dangerous source of error, the pipe being fed by the 
flow from springs, whose discharge must necessarily have been more or 
less irregular. Dr. Lampe, however, states to us in an explanatory letter, 
that he is satisfied no serious error could have arisen from this cause, 
there having been, directly preceding or during these intervals, no rains 
of consequence to notably affect the flow from the feeding springs; sub- 
sequent readings of the manometer, shortly after these intervals, also 
verified the constancy of flow. He considers that errors from this source 
will not change the given results more than one-half of 1 per cent. 

" Another source of error in these experiments arises from the fact 
that the pipe had two hydraulic grade lines. Although the several 
pressures were all determined above the anticlinal point at which these 
lines united, still the condition of the pipe was more or less unfavorable 
to extreme accuracy of observation, as the sucking or siphon action as 
the water passed over the summit could not have been perfectly regular, 
as doubtless the amount of air accumulating at this summit varied 
slightly from time to time ; the consequent intermittant sucking action 
of the water as it flowed below this summit, hence may have appreciably 
affected the nearest piezometers." 

EXPEEIMENTS OF NEVILLE. 

4 i Hydraulic Tables Co-efficients and Formulas," by John Neville, C. E. 

London, 1860-61. 

Mr. Neville states that the two experiments were the mean results of 
several experiments that were made by him with great care, with a pipe 
1.02 inches in diameter and 9.29 and 19.20 feet in length. Their tabular 
numbers are 59 and 60. 

Mr. Neville also ascertained that the co-efficient of contraction of the 
inlet end of the same pipe was 0.860, which corresponds to a co-efficient 
of influx of 0.352. This value was used by the writer in calculating the 
co-efficients of friction from these experiments. 

EXPERIMENTS OF PrOVIS. 

"Excerpt Minutes of Proceedings of the Institution of Civil Engineers." 

Vol. II, 1838. 

The experiments were made under the direction of W. A. Provis, 
M. Inst. C. E., with lead pipes 1.5 inches in diameter. Thirty-seven of 



42 WESTON ON FLOW OF WATER IN PIPES. 

them have been selected by the writer. Their tabular numbers are 175 
to 211 inclusive. 

The pipes were drawn in 15 foot lengths, and soldered together with 
care, so as to avoid as far as possible any interior obstructions. Into 
the upper end of the pipe was inserted a stop-cock of similar bore, and 
from this cock the length of the pipe was measured ; the opposite end 
of the cock was inserted into a cistern in which the surface of the water 
was maintained at a constant elevation during each experiment. The 
flow of water through the pipes, which discharged into the open air, 
was measured in a tank having a capacity of four cubic feet. 

Experiments were made with pipes 100, 80, 60, 40 and 20 feet long. 

The co-efficient of influx was not ascertained by Mr. Provis, and the 
writer, after having calculated two independent sets of experimental co- 
efficients of friction from the experiments that were made with the pipes 
100, 80 and 60 feefc long, by using 0.97 as a co-efficient of influx in one 
instance, and 0.505 in the other, finally determined to work out co-effi- 
cients of influx and loss from the experiments themselves. This was 
done by taking the data of the experiments made with the pipe 20 feet 
long, and working out co-efficients of influx and loss for different veloci- 
ties of flow for this length of pipe. The co-efficient of influx and loss 
thus determined were used in calculating the experimental co-efficients 
of friction of the experiments which were made with pipes 100, 80 and 
60 feet long, as a slight variation in its value one way or the other 
would not materially affect the results obtained from these experi- 
ments, on account of the long lengths of pipe used, and their low 
velocities of flow ; with the experiments made with the pipe 40 feet 
long, however, there seems to be a question of doubt, consequently 
they were not considered by the writer. The values of the experi- 
mental co-efficients of friction obtained by using this latter co-efficient 
of influx and loss, were in the majority of cases more than was ob- 
tained by using as a co-efficient of influx 0.97, and less than was 
obtained by using 0.505. The'lengths and heads of the pipes given in 
Table No. 1 are therefore less than those given by Mr. Provis ; the 
lengths by 20 feet, and the heads by an amount equivalent to the loss of 
head due to contraction at the entrance of the stop-cock, plus the loss of 
head due to friction in the stop-cock, and in a length of pipe 20 feet long. 

EXPEEIMENTS OF ROBISON. 

" Encyclopcedia Britannica. " 
The experiment is mentioned in an article on Rivers by Dr. John 
Robison, as having been made with a pipe 2 inches in diameter, and 
3 300 feet long, which was part of a compound pipe that was used to 
convey water from a spring into the town of Haddington. The nature 
of the pipe and the manner in which the experiment was conducted is. 
not given. Its tabular number is 237. 



WESTON ON FLOW OF WATER IN PIPES. 



43 



Experiments of Rennie. 
" Traite d? Hydraulique" by J. F. D'Aubuisson de Voisins. 

The two experiments were made with a lead pipe 0.5 inch in diam- 
eter and fifteen feet long. The manner in which they were conducted 
is not mentioned. Their tabular numbers are 28 and 29. 

Experiments of Simpson. 

" Excerpt Minutes of the Proceedings of the Institution of Civil Engineers.^ 

Vol XIV, Session 1854-55. 

The eighteen experiments were made under the direction of the late 
James Simpson, M. Inst. C. E., with pipes 12, 19 and 30 inches in diam- 
eter. Their tabular numbers are: 12 inch, 390 to 396 inclusive, 19 inch, 
423 to 427 inclusive, 30 inch, 467. 

Table No. I contains substantially all that Mr. Simpson mentioned 
in regard to the experiments. The following additional information, 
however, was furnished to the writer, in reply to some inquiries, by 
Mr. James Forrest, Secretary of the Institution of Civil Engineers : , 

" Mr. Arthur Telford Simpson, one of the sons of the late Mr. James 
Simpson, informs me that he cannot find the exact dates of the several 
experiments on the flow of water through pipes to which his father re- 
ferred in the discussion at their institution in 1855, but he gives the 
following statement of the time when the mains were laid, which will 
serve to show that they could not have been in use a very long time." 



Diameter in inches. 


Place. 


When laid. 


12 


Brixton to Streatham 


1848 


19 


Belvedere Road to Brixton 


1841 


12 


Liverpool 




12 


Carlisle 


1850 


30 


Ditton to Brixton 


1852 









Experiments of Smeaton. 

"Practical and Experimental Researches in Hydraulics,'''' by R. A. Pea- 
cock, G.E. 

The sixteen experiments were made by John Smeaton, an eminent 
English Civil Engineer, with a pipe l£ inches in diameter, and 100 feet 
long. The manner in which they were conducted and the nature of the 
pipe that was used are not mentioned. 

Their tabular numbers are 124 to 139 inclusive. 



44 WESTON" ON FLOW OF WATER IN PIPES. 

Experiments of Smith. 
" Transactions of the American Society of Civil Engineers." Vol. XII, 1883. 

The experiments were made under the direction of Hamilton Smith, 
Jr., M. Am. Soc. C. E., with pipes of various kinds, lengths and 
diameters. 

The writer has selected, and included in Table No. 1, only forty-two 
of the seventy-one experiments that were made by Mr. Smith. Twenty- 
seven of the remaining twenty -nine were omitted on account of having 
been made with small pipes, less than 64 feet in length, which had fun- 
nel shaped inlets, and two others on account of there being a question 
of doubt in regard to the discharge in one instance, and the diameter of 
the pipe used in the other. 

The fourty-two experiments were made with pipes of 0.502, 0.628, 
0.746, 1.054, 1.26, 10.93, 12.67, 14.76 and 16.99 inches in diameter. 

The experiments are described in divisions, which are preceded by 
the tabular numbers of the experiments, to which they refer. 

Nos. 365 to 369, 405 to 408 and 409 to 414, inclusive (10.93, 12.67 and 
14.76 inches), "were made at North Bloomfield, California, with their 
pipes laid side by side across a ravine about 100 feet lower than the pen- 
stock. They were made of single-riveted No. 14 sheet-iron; the rivet 
heads had worn pretty smooth, and no deduction for them was made in 
computing the areas. The pipes had been carefully coated when first laid 
with a mixture of coal tar asphaltum, and their interior surfaces at the 
time of these measurements were quite smooth. They were put together 
in slightly conical joints, the greatest variation in diameter being about 
I of an inch. The main joints were some 20 feet in length, put to- 
gether stove-pipe fashion, as is always done in the California hydraulic 
mines. The various heads wetfe obtained by adding to the length of 
the pipes at their outlets. " 

"The heads, lengths and mean diameters are given with exactness. 
The amount of discharge was measured by running the water over an 
iron weir, the co-efficients of whose discharge, with varying depths, had 
been carefully determined by absolute measurement, but at another 
point, and under conditions not exactly similar. This gauging was done 
with all the care practicable, the height of the water being measured 
with Boyden hook gauge, reading to 0.001 of an inch. The limit of 
possible error in these experiments is probably not over 2 per cent. " 

Nos. 407 and 408, " however, are somewhat unreliable, owing to the 
stoppage of a stone passing through the pipe. ' ' 

"The co-efficient of contraction is assumed at 1 in these pipes, as 
each of them had a short funnel-shaped inlet, which was included in 
the measurement of their lengths." 

In Nos. 369, 408 and 414, " the discharge was into a pool of water at 
the outlet box; in the other twelve the discharge was into the air." 



WESTON ON FLOW OF WATER IN PIPES. 45 

" There were two angles in the line of these pipes, one of 9 degrees and 
the other of 11 degrees; for the remainder of the distance they were nearly- 
straight; in the computations no deduction was made for these bends." 

Nos." 30 to 33, 41 to 46, 47 to 50, 78 to 84 and 140 to 144, inclusive 
(0.502, 0.628, 0.746, 1.05 and 1.26 inch), were made at New Almaden, 
California. "All these experiments were with straight pipes, and were 
made with considerable accuracy." 

"The mean diameters were computed by the weight of water con- 
tained in the pipes, taken by the sum of weights in the several joints, 
which varied slightly from the mean of the end diameters as directly 
measured. " 

" The discharge was determined by filling a tank of known size." 

" The iron gas pipes were joined by their usual couplings. The 
ends of the glass pipes were smoothly ground,, and a water-tight joint 
made by an outside rubber band. " 

" The wooden pipe was joined by usual plug couplings." 

Nos. 78 to 84, inclusive, were made with a pipe that was new and in 
good order. 

" The glass tubes were new and unscratched, of French manufacture, 
and somewhat conical." 

" The measuring tank held 15.2 cubic feet, and the times were de- 
terminated to one-fifth of a second." 

No. 422 (16.99 inch) "was with a new inverted siphon of double 
riveted sheet-iron pipe, with a pressure of about 800 feet at the lowest 
point, with a maximum tensile strain of 16 500 pounds per square inch, 
and with most of the joints made by sleeves with lead packing. It was 
coated with the usual mixture of coal-tar and asphaltum." 

" No deduction was made for rivet heads, which for over one-half 
the length doubtless formed noteworthy obstructions, as the pipe was of 
comparatively small diameter — 17 inches." 

" The mean diameter head and length are given with exactness. 
The discharge was measured first by the flow over a weir, and afterwards 
through standard apertures." 

" In all the experiments the actual or total head was either the 
difference in elevation between the surface of the water in the pen- stock 
and that in the outlet tank, or the difference between the water in the 
pen-stock and the center of the escaping jet, where the pipe discharged 
into the air." Experiments 30 to 33, 41 to 46, 47 to 50, 78 to 84 and 140 
to 144, inclusive " were made under the latter condition." 

ExPEKIMENTS OF STEAENS. 

" Transactions of the American Society of Civil Engineers" Vol. XIY, 1885. 

The four experiments were made by F. P. Stearns, M. Am. Soc. G. E., 
with a pipe 48 inches in diameter, and 17 472 feet long, belonging 



46 WESTON" ON FLOW OF WATER IN PIPES. 

to the Boston Water Works. Their tabular numbers are 513 to 516, 
inclusive. 

"The pipe was on the line of the Sudbury conduit. It was a cast- 
iron pipe coated with Dr. Angus Smith's coal-tar preparation. The 
changes in direction were made by two vertical curves, one of 500 and 
the other of 1 170 feet radius. The mean pressure on the pipes during the 
experiments was 41 feet. The pipes had been laid three years, and had 
been in use two, when the experiments were made, yet the tar-coating 
presented nearly as good a surface as when it was new. The volume 
flowing was measured at a weir about 10 miles distant up the conduit 
from the pipe, and to this measurment -n,- of a cubic foot per second was 
added for filtration into the conduit below the weir. The amount of the 
filtration was determined from fairly good data; but, even if somewhat 
inaccurate, it has little importance, as its whole effect was less than 1 
per cent. The weir used was 19 feet long, and had previously been 
tested by the actual measurement of the water passing over it. The loss 
of head in a length about 60 feet shorter than the whole length of the 
pipe was measured. This method was adopted to avoid including in the 
measurement the loss of head at the entrance of the pipe, the gain or 
loss at the exit, the effect of two rather sharp curves (30 feet radius), 
near the ends of the pipe, and several other disturbing causes. The 
apparatus used for taking the heads was as follows : In each of the pipe 
chambers, at either end of the pipe, there was a float gauge designed for 
permanent use in measuring the height of the water in the chambers. 
This consisted of a vertical iron cylinder, 12 inches in diameter, plugged 
at the bottom; in this cylinder was a hollow brass float, with a suitably 
guided stem, carrying an index up and down the face of a graduated 
scale. Water was admitted to the float cylinder through a small pipe 
leading from the center of the pipe chamber, the flow being controlled 
by a stop-cock. Connected with the float cylinder was a small brass cup, 
having a level top of known elevation. By filling the cylinder until the 
cup was even full, the position of the index was adjusted. For the pur- 
pose of these experiments, the small pipes leading from the float cylinders 
were extended into the ends of the 48-inch pipe, along its bottom about 
33 feet. The last 7 feet of each of these small pipes was a smooth, 
straight brass tube, with several holes drilled in its top, and with its end 
plugged." 

The heights of the gauges were carefully tested, and precautions 
taken to expel all air from the small pipes leading to them. 

Mr. Stearns was not able to conduct the experiments in person, but 
lie gave detailed instructions as to the work to be done, to two experi- 
enced assistants. 



WESTOK OK PLOW OF WATER IK PIPES. 47 

Experiments of Weisbach. 

*' The Mechanics of Engineering and of the Construction of Machines ," by 
Julius Weisbach, Ph.D. Translated from the German edition by 
Eckley B. Coxe, A.M. New YorTc, 1872. 

The experiments were made with pipes 0.409, 0.563, 0.972 and 1.27 
inches in diameter. 

Professor Weisbach only mentions the experimental co-efficients of 
friction (C) computed from the twenty-one experiments, and the nature 
and diameters of the pipes used in making the experiments. Their tab- 
ular numbers are, 0.409-inch and 0.563-inch, 1 to 14, inclusive; 0.972-inch, 
52 to 57, inclusive, and 1.27-inch, 145. 

Experiments of Weston. 

The five experiments were made by the writer during the years 1876 
and 1877 with pipes 0.97 and 6 inches in diameter, belonging to the 
Providence Water Works. 

The experiments that were made with each size of pipe are described 
separately, and each description is preceded by the tabular number or 
numbers of the experiment or experiments to which they refer. 

Six-inch. — Nos. 325 to 328 inclusive. An ordinary straight cast-iron 
pipe with socket joints, which were calked with lead and yarn in the 
usual way, was used in making these experiments. The pipe had been 
•coated when new by Dr. Angus Smith's process, and at the time the ex- 
periments were made it had been in service four years. 

The supply of water was taken from a main 30 inches in diameter, 
which was connected with the upper end of the pipe. 

Two very accurate hydraulic pressure gauges were used to determine 
the head ; the first was connected with the 6-inch pipe 500 feet from the 
30-inch main, and the second 1 170 feet from the first, and 410 from 
the lower end of the pipe where the discharge took place. The total 
length of the pipe was 2 090 feet. The difference in the readings of the 
two gauges, allowance having been made for their elevation, was taken 
as the loss of head due to friction for a length of 1 170 feet. 

The lower end of the pipe was connected with an 8-inch flush 
hydrant, which had a " chuck " with four lines of 2^-inch rubber hose 
about 100 feet long connected to it. The flow in the 6-inch pipe was 
regulated by opening and closing the valves of the " chuck." The first 
experiment was made with one valve open, the second with two, the 
third with three and the fourth with four. The discharge was ascer- 
tained by measuring the water flowing in the hose, which was done by 
connecting a hydraulic pressure gauge 1 foot from the hydrant to the 
line or lines of hose in use, and calculating the discharge from the 
pressure, a co-efficient of discharge having been previously determined 



48 WESTON ON FLOW OF WATER IN PIPES. 

by measuring the flow under different pressures, in a large tank ar- 
ranged expressly for the purpose.* 

Considerable time was devoted to making the observations, and a 
sufficient period was allowed for the water to get in train after each ex- 
periment, before commencing the next. The pipe had several side con- 
nections whic'i were carefully closed before the experiments were 
begun. 

0.969-inch. — No. 51. A new wrought-iron pipe, which had a layer of 
tin drawn through it for a lining, was used in making this experiment. 

The lengths were coupled together like ordinary gas pipe, with the 
exception that sheet tin bushings were fitted into the pipe at the joints 
to prevent any corrosion from penetrating into the interior, that might 
take place at the ends of the lengths where the iron was not covered 
with tin. 

The joints were carefully made, and the interior surface of the pipe 
was practically as smooth as the interior surface of an ordinary lead 
pipe. 

The pipe was 781.83 feet long, was laid nearly straight and was con- 
nected by a f-inch tap with a main 36 inches in diameter, which was 
directly supplied with water from a large reservoir. 

The diameter of the pipe was determined by measuring the diam- 
eters of a number of lengths. 

The difference between the surface of the water in the reservoir, and 
the center of the outlet end of the pipe which discharged into the open 
air, was taken as the head. 

The discharge was very accurately measured in a large tank. 

Three independent experiments were actually made, but as their re- 
sults are so nearly alike, their average only is given in Table No. 1. 

The co-efficient of influx and loss of head in the f-inch tap were 
ascertained by experimenting with a short piece of pipe connected to 
the tap, previous to making the experiment with the long pipe. 

A NEW FOEMULA FOE THE FLOW OF WATEE IN PIPES 
HAVING VEEY SMOOTH INTEEIOE SIDES FEOM \ TO 3i 
INCHES IN DIAMETEE. 

Before proceeding any further, it may be well to repeat, that, for 
reasons already mentioned, the basis of investigation which was adopted 
by the writer at the commencement of his researches, is the co-efficient 
of friction C, which is a factor of the equation, 

I v 2 

Consequently, the investigations which will now be described, as well as 

♦Transactions Am. Soc. C. E., Vol. XIII, 1884. Weston on the Flow of Water through 
Rubber Hose. 



WESTOK ON FLOW OF WATER IK PIPES. 49 

those which will be mentioned hereafter, have been entirely devoted to 
the determination of a formula for the co-efficient of friction £. 

It .was found, by consulting Table No. 1, that there were two hun- 
dred and thirty-eight experiments that had been made with twenty- 
seven different pipes having very smooth interior sides; one hundred 
and ninety-one of these experiments were made with pipes of lead, 
glass, zinc, tin, and sheet-iron coated with bitumen from 0.41 inch to 
3.25 inches in diameter; eighteen that had been made with pipes of 
sheet-iron coated with bitumen 7.72 and 11.22 inches in diameter; thir- 
teen that had been made with new gas pipe from 0.63 to 1.05 inches in 
diameter; and sixteen that had been made with a pipe 1.25 inches in 
diameter, the nature of which the writer has not been able to ascertain, 
although it evidently had smooth interior sides. 

The last twenty-nine experiments mentioned, that were made with 
iron pipe, etc., were not given the same weight in the investigations as 
those that had been made with pipes which were known to have very 
smooth interior sides, but were more especially used for the purpose of 
substantiating the laws and results obtained with the latter. 

Then, as pipes of 7.72 and 11.22 inches in diameter having very 
smooth interior sides are rarely used, and as the laws that seemed to 
apply to the results of the experiments that were made with the pipes 
of these diameters were slightly at variance with the laws that applied 
to the others, it was decided to consider only the experiments that were 
made with the pipes of the smaller sizes, in constructing the new for- 
mula, and to limit its application so as to include only pipes from 0.40 to 
3.50 inches in diameter. (An independent formula was also determined 
by the writer for the two pipes, 7.72 and 11.22 inches in diameter, 
which will be mentioned hereafter.) 

The diagrams which refer to this formula are numbered from 1 to 
14, the first six being devoted to illustrating the method by which the 
formula was constructed, and the last eight to its comparison after 
completion. 

For convenience of investigation, when it could be done without 
affecting the results sought after before reaching the fourth decimal 
place, the larger part of the experimental results that were obtained 
with pipes having diameters which were very nearly alike, were classified 
in each instance, under a common nominal diameter, as will be seen 
upon the diagrams. 



50 WESTON ON FLOW OF WATER IN PIPES. 

The nominal diameters of the pipes that were used in making the 
experiments, the results of which were employed in constructing the 
formula, etc., the numbers that the experiments are given in Table No. 
1, and the numbers of the diagrams upon which the results are platted, 
are as follows: 

0.5-inch: Tabular numbers 1 to 14, 28 to 29, 34= to 46. Diagrams 
Nos. 1 and 7. 

0. 75-inch : Tabular numbers 47 to 50. Diagram No. 8. 

1.0-inch: Tabular numbers 51 to 60, 78 to 123. Diagrams Nos. 2 
and 9. 

1.25-inch: Tabular numbers 124 to 139 and 145. Diagrams Nos. 
3 and 10. 

1.50-inch: Tabular numbers 146 to 160, 175 to 211, 224 to 230. Dia- 
grams Nos. 3 and 11. 

2.13-inch: Tabular numbers 231 to 249. Diagrams Nos. 4 and 12. 

2.50-inch: Tabular numbers 250 to 269. Diagrams Nos. 4 and 13. 

3.25-inch: Tabular numbers 296 to 307. Diagrams Nos. 5 and 14. 

The results of any of the experiments that were made with velocities 
of less than 1 foot per second were not used in the actual construction 
of the formula, however, owing to the influence that minute errors of ob- 
servation have upon results obtained with low velocities. For example, 
an error of 0.01 foot in observing the loss of head, in making an experi- 
ment with a pipe 1 inch in diameter and 100 feet long, when the velocity 
of flow was 0.25 feet per second, would affect the value of the co-effi- 
cient of friction to a greater extent than would an error of 1.5 feet in 
observing the loss of head, in making an experiment with the same 
pipe when the velocity of flow was 10 feet per second. The results 
shown on the diagrams from No. 1 to No. 5, that were obtained with 
velocities less than 1 foot per second, were platted after the formula was 
completed for the purpose of verification and comparison. 

The first steps that were taken in the construction of the formula 
were to determine the conditions upon which the co-efficient of friction 
£ was dependent, and after considerable preliminary platting, computa- 
tion and study, it was found to be dependent, in this instance, upon both 
the diameter and the square root of the velocity. 

The process by which the formula was finally developed, after the 
laws that applied to it had been ascertained by a method somewhat sim- 
ilar, is illustrated by Figs. 1 and 2, and upon the diagrams from No. 1 
to No. 6. 



WESTON ON" FLOW OF WATER IN PIPES. 



51 



Fl 




An independent formula £ = a -j- 



/i 



*/v 



was first determined for each 



diameter of pipe that the experimental data embraced. 

The numerical values of a and /? were deduced graphically in the 
following manner by the aid of the expression C +/v, which is the equa- 
tion of the straight line o Jc, Fig. 1 (and the average lines shown upon 
the diagrams from No. 1 to No. 5), whose abscissae are the values of ^v, 
and whose ordinates are the values of £ \/v~. 

A line was drawn upon the lower part of a large sheet of paper, with 
a sharp pointed lead pencil, as an axis of abscissae, and another line 
drawn in the same way at right angles to it, at its left extremity, as 
an axis of ordinates. 

Then at a scale of 1 inch to 4 feet the square roots of the velocities 
(v/^T) that were used in computing the experimental co-efficients of 
friction (Q were platted as abscissae, and the experimental co-efficients 
of friction multiplied by the square roots of their respective velocities 
(C \/v ) platted as ordinates, at such a scale that four decimal places could 
be easily read. 

At the upper extremity of each ordinate a small circle or symbol was 
drawn in ink, as shown on the diagrams from No. 1 to No. 5, in order to 
render it conspicuous, and to designate the results obtained from the 
experiments of each authority. 

If all of the minute errors could have been detected, that were, pre- 
sumably, made in conducting the experiments from which the platted 
results were obtained, and if the conditions relative to the diameters and 
the interior sides of the different pipes that were used had been pre- 



52 WESTON ON FLOW OF WATER IN PIPES. 

cisely the same, and if the laws upon which the formulas were based were 
absolutely correct, all of the circles or symbols upon each diagram from 
No. 1 to No. 5, would be in a true inclined line. As it is not possible to 
realize all of these theoretical conditions in actual practice, however, it 
was always necessary to draw an average line through the circles or 
symbols, as shown upon the diagrams from No. 1 to No. 5. This line was 
located by the aid of a piece of fine thread, and its position was gener- 
ally such a very difficult matter to determine, that it was often not satis- 
factorily accomplished until after a number of trials. 

When the average line was drawn, it was extended through the axis 
of ordinates to a prolongation of the axis of abscissae, and the distance x, 
Fig. 1, scaled on this prolongation, from the point where the average line, 
intersects it, to the axis of ordinates. A line was also drawn with a fine 
pointed lead pencil as an ordinate, from a point corresponding to the 
square root of some high velocity, at the extreme right of the axis of 
abscissae, and the distance y, Fig. 1, between the axis of abscissae and the 
average line, scaled upon it. Then the value of (5 was ascertained by 
scaling the distance on the axis of ordinates between the axis of abscissae 
and the average line, Fig. 1, and the value of a, which is the tangent 
of the angle hep, determined thus, 

V v x 

and the expression for the co-efficient of friction C, becomes for each 
diameter of pipe, 

^i^£. + -4 = =±+ -£= = « + 



For example, let 
/3 = 0.0283, y = 0.0622, vV= 3 > * = 1.347, and C = 0.0113 + 2i5?£? 

When a formula for each diameter had been determined in the man- 
ner just described, it was found by taking the values of a and /3, and 
platting them in a similar manner, and with the same degree of care, 
the diameters as abscissae, and the corresponding values of a and ft as 
ordinates, the extreme upper points of which were enclosed in circles, 
and drawing an average line from the axis of ordinates through the 
circles representing each as shown upon Diagram No. 6, that a was 
constant for all diameters and velocities, and that /3 decreased slightly 
as the diameters increased. The value of a, being constant, was ascer- 



WESTON ON FLOW OF WATER IN PIPES. 



53 



tainedlby simply scaling the distance, which was found to be 0.0126, be- 
tween the axis of abscissae and the average line, they being parallel 
in this instance. The value of the diametric co-efficient, which we will 
call 2, upon which (5 is dependent, was determined . by measuring the 
distance b, Fig. 2, on the axis of ordinates between the axis of abscissae 



Fi 3 . Z 




and the average line, and by drawing a line as an ordinate from the 
abscissa representing the greatest diameter, and scaling upon it the dis- 
tance c, Fig. 2, between the axis of abscissae and the average line, and 
using their values in this form, 

b—c 0.0315—0.014 n nn . 

z = = = 0.005 

d 3.5 

and the expression for /3 becomes 

/3 = b—d z, 

and^the formula for the co-efficient of friction C, for all diameters from 
0.40 to 3.5 inches, and for all velocities 

0.0315— d 0.005 



C = 0.0126 -f- 



Vv 



On account of the numerical values of the diameters having been 
used in inches in determining this formula, it can only be used in its 
present form when the diameter, d, is expressed in inches. (This is the 
only instance, with the exception of the cases when the same formula is 
shown upon the diagrams from No. 6 to No. 14, that any formula con- 
tained in this paper is given in measures other than feet. ) 



54 WESTON" ON" FLOW OF WATER IN" PIPES. 

The formula therefore becomes, for measures in English feet, 

C = 0126 4- Q- 0315 -^ - 06 

v/ v 

and V = C0.0126 + 0-0815-tf 0.08 V L*. 

Diagrams from No. 7 to No. 14 show a comparison of this formula with 
the original experimental results from which it was derived, as well as 
with a number of other experimental results that were not used in con- 
structing the formula. 

Co-efficients of friction (Q, that have been worked out from several 
well-known formulas for the flow of water through pipes, by different 
authorities are also platted for comparison on the diagrams from No. 7 
to No. 15. 

The equations for computing these last mentioned co-efficients of 
friction, as arranged by the writer, are as follows: 

From the formula of Prony, 

C = 0.02733 + 0^04464. 

V 

From the formula of Eytelwein, 

C = 0.0220 + a005754 - 

V 

From the formula of Darcy, 

C = 0.01989 4- Q - 001666 . 
d 

From the formula of Weisbach, 

C = 0.01439 + °4^°i. 

V V 

Equations for the flow of water in pipes, in which the co-efficient 
of friction £, worked out by this formula, is used, will not admit of 
a direct solution, but the co-efficients should be first determined for 
different values of the velocity and tabulated, after which the true value 
of the velocity can be determined by finding an approximate value, and 
thence taking out the corresponding co-efficient from the table, which 
does not vary to any considerable extent for small changes of velocity. 

The writer would have been much better satisfied had he been able 
to construct a formula that could be more easily solved than the one he 
has presented, but as his principal object was accuracy and not sim- 
plicity, he could not do this and conform satisfactorily to the experi- 
mental results. 



WESTON" ON" FLOW OF WATER IK PIPES. 



55 



The new formula will not be further discussed, as its merits or de- 
merits are plainly set forth upon the diagrams upon which it is platted. 

The following table gives the co-efficients of friction (C), for pipes 

having very smooth interior sides from 0.5 to 3.5 inches in diameter, 

and for velocities from 0.10 to 50 feet per second, calculated by the 

formula. 

0.0315 — d 0.06 



£ = 0.0126 + 



V v 



Co-EFFICTENT OF FfUCTION £. 





Diameter op Pipes in Feet and Inches. 


Velocity in 




feet per 






















second. 


0.0417 


0.0521 


0.0625 


0.0833 


0.1042 


0.1250 


0.1667 


0.2083 


0.2500 


0.2917 




% 


/8 


% 


1 


1# 


1* 


2 


2X 


3 


3^ 


0.10 


0.1043 


0.1023 


0.1004 


0.0964 


0.0924 


0.08S5 


0.0806 


0.0727 


0.0648 


0.0569 


0.50 


0.0536 


0.0527 


0.0518 


0.0501 


0.0483 


0.0465 


0.0430 


0.0395 


0.0359 


0.0324 


1.00 


0.0416 


0.0410 


0.0404 


0.0391 


0.0379 


0.0366 


0-0341 


0.0316 


0.0291 


0.0266 


1-20 


0.0391 


0.0385 


0.0381 


0.0367 


0.0356 


0.0343 


0.0319 


0.0296 


0.0274 


0.0250 


1-40 


0.0371 


0.0365 


0.0363 


0.0347 


0.0338 


0.0324 


0.0304 


0.0283 


0.0262 


0.0239 


1.60 


0.0356 


0.0348 


0.0350 


0.0332 


0.0323 


0.0312 


0.0292 


0.0272 


0.0252 


0.0232 


1.80 


0.0342 


0.0336 


0340 


0.0321 


0.0313 


0.0302 


0.0284 


0.0265 


0.0246 


0.0226 


2.00 


0.0331 


0.0327 


0.0322 


0313 


0.0305 


0.0296 


0.0278 


0.0260 


0.0243 


0.0225 


2.50 


0.0310 


0.0306 


0.0300 


0,0294 


0.0286 


0.0278 


0.0262 


0.0246 


0.0230 


0.0214 


3 00 


0.0293 


0.0290 


0.0286 


0.0279 


0.0272 


0.0265 


0.0250 


0.0236 


0.0221 


0.0207 


3.50 


0.0281 


0.0278 


0.0274 


0.0268 


0.0260 


0.0254 


0.0242 


0.0228 


0.0214 


0.0201 


4.00 


0.0271 


0.0268 


0.0265 


0.0259 


0.0252 


0.0246 


0.0234 


0.0221 


0.0209 


0.0196 


4.50 


0.0263 


0.0260 


0.0256 


0.0251 


0.0244 


0.0238 


0.0227 


0.0216 


0.0204 


0.0192 


5.00 


0.0256 


0.0253 


0.0250 


0.0244 


0.0238 


0.0233 


0.0222 


0.0211 


0.0200 


0.0189 


5.50 


0.0250 


0.0246 


0.0244 


0.0238 


0.0234 


0.0228 


0.0218 


0.0207 


0.0196 


0.0186 


6.00 


0.0244 


0.0242 


0.0239 


0234 


0.0229 


0.0224 


0.0214 


0.0204 


0.0193 


0.0183 


6.50 


0.0240 


0.0236 


0.0235 


0.0230 


0.0225 


0.0220 


0.0210 


0.0200 


0.0190 


0.0181 


7.00 


0.0236 


0.0233 


0.0230 


0.0226 


0.0222 


0.0217 


0.0207 


0.0198 


0.0188 


0.0179 


7.50 


0.0232 


0.0229 


0.O227 


0.0222 


0.0218 


0.0214 


0.0204 


0.0195 


0.0186 


0.0177 


8.00 


0.0229 


0.0226 


0.0224 


0.0220 


0.0215 


0.0211 


0.0202 


0.0193 


0.0184 


0.0175 


8.50 


0.0225 


0.0223 


0.0221 


0.0216 


0.0212 


0.0208 


0.0200 


0.0191 


0.0182 


0.0174 


9.00 


0.0222 


0.0220 


0.0218 


0.0214 


0.0210 


0.0206 


0.0198 


0.0189 


0.0181 


0.0173 


9.50 


0.0220 


0.0218 


0.0216 


0.0212 


0.0208 


0.0204 


0.0196 


0.0188 


0.0180 


0.0172 


10 


0.0218 


0.0216 


0.0214 


0.0210 


0.0206' 


0.0202 


0.0194 


0.0186 


0.0178 


0.0170 


■ 11 


0.0214 


0212 


0.0210 


0.0206 


0.0202 


0.0198 


0.0191 


0.0184 


0.0176 


0.0168 


12 


0.0210 


0208 


0.0206 


0.0203 


0.0199 


0.0195 


0.0188 


0.0181 


0.0174 


0.0166 


13 


0.0206 


0.0205 


0.0203 


0.0199 


0.0196 


0.0193 


0.0186 


0.0179 


0.0172 


0.0165 


14 


0.0204 


0.0202 


0.020-1 


0.0197 


0.0194 


0.0190 


0.0184 


0.0177 


0.0170 


0.0164 


15 


0.0201 


0.0200 


0.0198 


0.0195 


0.0191 


0.0188 


0.0182 


0.0175 


0.0168 


0.0162 


16 


0.0199 


0.0197 


0.0195 


0.0192 


0.0189 


0.0186 


0.0180 


0.0174 


0.0167 


0.0161 


17 


0.0196 


0.0195 


0.0194 


0.0190 


0.0187 


0.0184 


0.0178 


0.0172 


0.0166 


0.0160 


18 


0.0194 


0.0193 


0.0192 


0.0188 


0.0186 


0.0183 


0.0177 


0.0171 


0.0165 


0.0159 


19 


0.0193 


0.0191 


0.0190 


0.0187 


0.0184 


0.0181 


0.0175 


0.0169 


0.0164 


0.0158 


20 


0.0191 


0.0189 


0.0188' 


0.0185 


0.0182 


0.0180 


0.0174 


0.0168 


0.0163 


0.0157 


25 


0.0184 


0.0183 


0.0182 


0.0179 


0.0177 


0.0174 


0.0169 


0.0164 


0.0159 


0.0154 


30 


0.0179 


0.0178 


0.0177 


0.0174 


0.0172 


0.0170 


0.0165 


0.0161 


0.0156 


0.0152 


35 


0.0175 


0.0174 


0.0173 


0.0171 


0.0169 


0.0167 


0.0102 


0.0158 


0.0154 


0.0150 


40 


0.0172 


0.0171 


0.0170 


0.0168 


0.0166 


0.0164 


0.0160 


0.0156 


0.0152 


0.0148 


50 


0.0167 


0.0166 


0.0165 


0.0168 


0.0162 


0.0160 


0.0156 


0.0153 


0.0149 


0.0146 



The formula for a co-efficient of friction C for the two sheet-iron 
pipes, coated with bitumen, 7.72 and 11.22 inches in diameter, that has 
previously been mentioned, and which was constructed in a manner 



56 WESTON ON FLOW OF WATER IN PIPES. 

similar to the one that has just been described, is constant for both 
diameters, and is dependent only upon the square root of the velocity 
(«/ v ), viz. : 

t = 0.0126 + °-°^ 5 • 

This formula is platted for comparison with the experimental results 
from which it was determined (which are numbered from 338 to 348, and 
from 370 to 376 in Table No. 1), upon Diagrams Nos. 23 and 24. 

FORMULAS FOR THE FLOW OF WATER IN PIPES HAVING 
INTERIOR SIDES SIMILAR TO NEW CAST-IRON PIPES. 

An examination of Table No. 1 led the writer to the conclusion that 
there were one hundred and eighty-eight experiments which it would 
be advisable to utilize in constructing a formula for the flow of water 
in pipes having interior sides similar to new cast-iron pipes, that had 
been made with twenty-eight different pipes from 0.48 to 90 inches in 
diameter. 

It was very difficult in a number of instances to determine the number 
of years of service that should limit what would generally be called a 
new or clean pipe, especially if the experiments under consideration 
had been made with pipes that were not originally coated with coal tar, 
or some preparation of a similar nature, unless there was positive evi- 
dence of the exact condition of their interior sides at the time that the 
experiments were made, as it has been demonstrated by chemical 
analysis that the interior sides of cast-iron pipe oxidize much faster 
with slightly alkaline and aerated waters flowing through them than 
they do with other waters differently constituted. In the absence of 
more reliable data, the writer has generally been governed in cases of 
this kind by the values of the co-efficients of friction (Q. 

After carefully studying and platting the experimental results in a 
manner similar to that mentioned in the description of the construction 
of " A new formula for the flow of water in pipes having very smooth 
interior sides," the writer made up" his mind that he could not construct 
a formula that would compare as satisfactorily with the experimental 
results, as two formulas by Henry Darcy, which are to be found on pages 
254, 258 and 368 of his work entitled "Recherches experimentales rela- 
tives au mouvement de l'eau dans les tuyaux." 



WESTON ON FLOW OF WATER IN" PIPES. • 57 

The formulas for obtaining the co-efficients of friction (C), which is a 
factor of the equation li f = C \ ^ as worked out from these for- 
mulas (Darcy's) by the writer, and reduced to English measures are as 

follows : 

0.00166573 
C == 0.0198920 H ^ " 

0.0040723 + 0^0020816. 



C = 0.017879+ 0^?66 + . -^ 

Darcy recommends the formula from which the first formula for the 
co-efficient of friction £ was deduced, for general use, and it is ordi- 
narily known as "Darcy's formula." As may be seen in the first for- 
mula, the value of the co-efficient C is entirely dependent upon the 
diameter of the pipe. Darcy did not fail to recognize, however, that the 
velocity also entered into the problem, but considered (after analyzing 
the experimental results from which the formula was derived), that 
when the velocity is more than 0.33 feet per second, especially if the 
pipes have been in use a short time, the term relative to it, which would 
enter into the formula for the coefficient of friction & could be entirely 
eliminated, without the reliability of the formula being appreciably 
affected. The formula, from which the second formula for a co-efficient 
of friction Cwas deduced, was intended by Darcy to be used for all 
velocities, and to apply more especially to new pipes. (The same 
experimental results were used in constructing both of these formulas.) 
The experimental co-efficients of friction (Q that were worked out 
from the one hundred and eighty-eight experiments, and co-efficients of 
friction worked out from Darcy's formulas, and several other well- 
known formulas, are platted for comparison on diagrams from No. 15 
to No. 22, and on No. 25. 

The formulas for obtaining the co-efficients of friction from the 
formulas last mentioned, as arranged by the writer (the first three of 
which have previously been referred to), are as follows: 
From the formula of Prony, 

C = 0.02733 + °- 004464 

V 

From the formula of Eytelwein, 

t = 0.0220 + °- 005754 - 






58 WESTON ON FLOW OF WATER IN PIPES. 

From the formula of Weisbach, 

C = o.01439 + 2^i 

y v 

From the formula of Kutter, 

2# 



t = 



20 83 4- °- 9056 + °- 00140S 



n J 



1+ Al.66 + a0028075 )^L 
^ J ' J d 

For facility of investigation, when it could be done without affecting 
the results sought after before reaching the fourth decimal place, the 
greater part of the experimental results that were obtained with pipes 
having diameters very nearly alike were classified under a common 
nominal diameter, as will be seen upon the diagrams . 

The nominal diameters of the pipes that were used in making the 
experiments, the results of which are platted on the diagrams, the num- 
bers that the experiments are given in Table No. 1, and the numbers of 
the diagrams upon which the results are platted, are as follows: 

0.48-inch, Tabular numbers 15 to 27. Diagram No. 25. 
1.047-inch, Tabular numbers 61 to 77. Diagram No. 25. 
1.55-inch, Tabular numbers 212 to 223. Diagram No. 25. 
3.22-inch, Tabular numbers 283 to 295. Diagram No. 15. 
5.39-inch, Tabular numbers 309 to 328. Diagram No. 16. 
7.40-inch, Tabular numbers 329 to 337. Diagram No. 17. 
11.69-inch, Tabular numbers 365 to 369, 377 to 396, 405 to 408. Dia- 
gram No. 18. 
15.00-inch, Tabular numbers 409 to 422. Diagram No. 19. 
19. 69 -inch, Tabular numbers 423 to 456. . Diagram No. 20. 
30 .00-inch, Tabular numbers 467 to 485. Diagram No. 21. 
48.00-inch, Tabular numbers 513 to 517. Diagram No. 21. 
90.00-inch, Tabular numbers 518 to 520. Diagram No. 22. 

There are platted upon diagrams Nos. 18, 19, 20 and 21, a number of 
experimental results that should probably not be given as much weight 
in making a comparison, as the other experimental results which are 
platted upon the same diagrams, viz. : Upon diagram No. 18, the results 
that were obtained from ten of the experiments made by Simpson, on 
account of old pipe having been used; upon diagrams Nos. 19 and 
20, the results obtained from three of the experiments made by the 
Edinburgh "Water Company, and five of the experiments made by Simp- 
son, for the same reason; and upon diagram No. 21, the results obtained 



WESTON ON FLOW OF WATER IN PIPES. 59 

from eighteen experiments made by Darrach with pipes 30 inches in 
diameter, on account of allowances that had to be made, in computa- 
tion, for" the resistance of check-valves which were located upon the 
pipes. 

As will be seen by an examination of the diagrams, the co-efficients of 
friction (0 worked out from Darcy's formulas agree very well in the major- 
ity of cases with the experimental results, and much better than any 
of the other formulas that are platted. Therefore, in the opinion of the 
writer, the formulas of Darcy are safe and reliable to use in general 
practice. The former, which is represented by a straight line on the 
diagrams, for velocities including and exceeding 0.33 feet per second, 
and the latter, which is represented by a curved line on the diagrams, 
for velocities of less than 0.33 feet per second. The former is also to be 
recommended for its simplicity, as well as for its accuracy, and also 
for the convenience with which it can be used in both the simple and 
extended forms of equations previously mentioned and recommended 
by the writer, for the flow of water in pipes. 

Of the other co-efficients of friction (£), that are platted on the dia- 
grams, which have been worked out from the formulas of different 
authorities, the writer will only mention in detail those that have been 
derived from the well-known and very valuable formula of Kutter, which 
during the last few years has been so much discussed and extensively 
used for computing the flow of water through masonry conduits. There 
seems to be a general impression among a number of engineers that this 
formula can be applied to iron pipes, although Kutter does not give any 
co-efficients of roughness, in connection with it, which were obtained 
from experiments that were made with iron pipes. In order to ascertain 
if this impression was correct, the writer used in computing the results 
for comparison for this formula, three co-efficients of roughness as given 
by Kutter, which in his opinion would be the most likely to apply to iron 
pipes, viz. : 0.010 which is for a surface of plaster in pure cement, 0.011 
which is for a surface of plaster in cement with one-third sand, and 0.013 
which is for a surface of brickwork or ashlar. The results obtained by 
using these three co-efficients of roughness are platted on the diagrams 
from No. 16 to No. 22, and in the writer's opinion neither of them 
compare as favorably with the experimental results as the formulas of 
Darcy; also the same co-efficient of roughness seems not to apply to 
all sizes of pipe, for instance, 0.010 applies best to pipes having nomi 



60 WESTON ON FLOW OF WATER IN" PIPES. 

nal diameters of 5.39 and 7.40 inches, 0.011 to pipes having nominal 
diameters of 11.69, 16 and 19.69 inches, and 0.013 to pipes having diam- 
eters of 30 and 48 inches. 

The results obtained from the experiments made by Clarke with a 
brick tunnel 90 inches in diameter are simply platted on Diagram No. 
22, in order to show to what an extreme range of diameters the formulas 
of Darcy can be safely applied. 

OLD CAST-IKON PIPES LINED WITH DEPOSIT, AND THE 

SAME CLEANED. 

It was found by examining Table No. 1 that there were fifty-eight 
experiments that had been made with eight different old cast-iron pipes 
lined with deposit, from 1.43 to 36 inches in diameter, and twenty-two 
experiments that had been made with three of these pipes after they had 
been cleaned. 

A preliminary study of the results obtained from the experiments 
that were made with the old cast-iron pipes lined with deposit con- 
vinced the writer that he could not satisfactorily construct a general 
formula from the data at hand. He was able, however, to construct 
three individual formulas for co-efficients of friction (£). In one instance 
with two sets of results obtained from experiments made with two 
different pipes of the same diameter, and in two instances with three 
sets of results obtained from experiments made with three different 
pipes of the same diameter, which are as follows : 

For 20-inch pipe, C =0.0156 + ^il?. 

159 
For 36-inch pipe, C = 0.0143. 

v 

1835 
For 36-inch pipe, C = — 0.0225. 

v 

(The same experimental results were used in constructing the two 
latter formulas.) 

All of the co-efficients of friction (Q that have been derived from 

experiments that were made with old pipes lined with deposit (with the 

exception of ten that were obtained from experiments made with one 

pipe 30 inches in diameter), are platted upon diagrams Nos. 26 and 28, 

for comparison with these formulas, and with one worked out by the 

writer from a formula by Darcy for the flow of water in pipes slightly 

encrusted with deposit, viz., 

C = 0.03978 +™ 
d 



WESTCXN" ON FLOW OF WATER IN" PIPES. 61 

As the writer does not consider these formulas for old pipes lined 
with deposit of much value, they will not be further discussed. 

The results that were obtained from experiments that were made 

with old cast-iron pipes after having been cleaned, are simply platted 

on diagram No. 27 for the purpose of comparing them with the 

formula for a co-efficient of friction C, worked out from a formula 

by Darcy for the flow of water in new cast-iron pipes, which has been 

previously mentioned, viz., 

0.00166573 



C = 0.019892 + 



d 



The diameters of the pipes that were used in making the experi- 
ments, the results of which have just been mentioned, the numbers that 
the experiments are, given in Table No. 1, and the numbers of the dia- 
grams upon which the results are platted, are as follows: 

1.43-inch, Tabular numbers 161 to 174. Diagrams Nos. 26 and 27. 
3.15-inch, Tabular numbers 270 to 282. Diagrams Nos. 26 and 27. 
9. 63-inch, Tabular numbers 349 to 364. Diagrams Nos. 26 and 27. 
20.00-inch, Tabular numbers 457 to 466. Diagram No. 26. 
30.00-inch, Tabular numbers 486 to 495. (Not platted.) 
36.00-inch, Tabular numbers 496 to 512. Diagram No. 28. 

THE CO-EFFICIENTS OF RESISTANCE OF THE FLOW OF 
WATER IN PIPES FOR ENLARGEMENTS, CONTRACTIONS, 
ELBOWS AND CURVES. 

Should the forms of formulas that have been recommended by the 
writer for the flow of water in pipes, be used and extended to cover con- 
ditions other than those relating to straight pipes, one or more of the 
four co-efficients of resistance, for enlargements, contractions, elbows 
and curves, will probably be required, in order to do so. Therefore, as 
the writer has not anything original to present pertaining to these co- 
efficients, he has taken the following data relating to them, nearly entire, 
from the valuable work of Professor Weisbach, entitled, "A Manual 
of the Mechanics of Engineering and of the Construction of Machines," 
which was translated from the fourth German Edition, by E. B. Coxe, 
A. M., in 1872. 

Sudden Enlargement. 



/<=(|r-l), \f 



'/ = »%■ 



62 



WESTON ON" FLOW OF WATER IN" PIPES. 



Fi 3 . 3. 



I 



F 



F 



The following table is calculated according to the formula. 



F 

F x 


1.1 


1.2 


1.3 


1.4 


1.5 


1.6 


1.7 


1.8 


1.9 


M 


.01 


.04 


.09 


.16 


.25 


.36 


.49 


.64 


.81 



F 

Fi 


2.0 


2.5 


3.0 


3.5 


4.0 


5.0 


6.0 


7.0 


8.0 


M 


1.00 


2.25 


4.00 


6.25 


9.00 


16.00 


25.00 


36.00 


49.00 



Contraction. 

Fig. 4. 



\ 



I 7 



F, 



I 



but <p is increased by the resistance at the entrance into the pipe and by 
the friction of the water in the interior portion of the tube, to 0.505. 



Elbows. 
r = 0.9457 sin ?£■ + 2.047 sin ^-, li f = r -* 




M 



2 



*9 






STJiiSi 

:; '' :, #h ~r7Ti--- 




^S 



tilii 



Z> 



WESTON ON FLOW OF WATER IN" PIPES. 



63 



The following table contains a series of co-efficients of resistance cal- 
culated, according to the formula, for different angles of deviation : 



p 

2 


10° 


20° 


30° 


40° 


45° 


50° 


55° 


60° 


65° 


70° 


r 


.046 


.139 


.364 


.740 


.984 


1.260 


1.556 


1.861 


2.158 


2.431 



If to one elbow AGB, Fig. 6, another elbow is joined, as is shown in 
Figs. 7 and 8, a peculiar but at the same time easily explicable phenom- 
enon of efflux is observed. The elbow BDE, Fig. 7, which turns 
the stream to the same side as the elbow AGB, Fig. 6, produces no 
further contraction of the stream, and, therefore, for efflux with full 
cross section, r is no greater than for a simple elbow AGB. But if the 
other elbow BDE, Fig. 8, turns the stream to the opposite side, the 
contraction is a double one, and the co-efficient of resistance is conse- 
quently twice as great as for a single elbow. If, finally, BDE is so 
joined to AGB that DE stands at right angles to the plane ABB, r then 
becomes about one and one-half times as great as for the single elbow 
AGB. 

Curved Pipes. 
For curved pipes with circular cross-sections : 

i, = 0.131.+ 1.847 (JJL)*, V =*-g- 



A 



fig ?. 



ttg /o, 



uFt^./e. 




The following table is calculated according to the formula: 



d 
~2r~ 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


i 

0.9 1.0 

i 


i> 


.131 


.138 


.158 


.206 


.294 


.440 


.661 


.977 


1.408 1.978 



64 WESTON ON FLOW OF WATER IN PIPES. 

If one curve BB, Fig. 10, is terminated by another, which turns the 
stream further in the same direction, if eg, the axis of the pipe forms a 
semicircle, like BBE, Fig. 11, the contraction is not changed and t]> has 
the same value as for the pipe in Fig. 10, which forms a quadrant. If, 
on the contrary, a curve BE, Fig. 12, which turns the stream in the 
opposite direction, is attached to the first one, an eddy is formed between 
the two, and a second contraction of the stream takes place by which 
the resistance (if?) is nearly doubled. 



PLATE i 
TRANS. AM. SOC. CiV. ENG'RS. 
VOL. XXli-N? 431 



WESTON 

O N 

FLOW OFWATER IN PIPES 



1 ' T~ 



^Dt<z&r€Z7?z, tJVa.j. 



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PLATE I! 

TRANS. AM. SOC. CIV. ENG'RS. 

VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



^Z? €ccg77"cz 7??s i/Ya *& . 




PLATE III. 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 
O N 
LOW OFWATER IN PIPES 



^Z)6cL£?7"CC7?Zs k/Yo. t5* 




PLATE IV 
TRANS. AM. SOC. CIV, ENG'RS. 
VOL. XXII. N? 431 



WESTO N 

O N 

FLOW OF WATER !N PIPES 



jDiLcLgr7°a,7n, *7Yb. ■£ . 




PLATE V WESTON. 
TRANS. AM. SOC. CIV. ENG'RS. ON 

VOL. XXII. IN? 43! FLOW OF WATER IN PIPES 






ft, £ -ft *€ »57Tft * ft 
ft ft S^ft ft ^ 


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PLATE VI 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OFWATER IN PIPES 



JDZ&U?T*CC?9Z, JYo. 6. 



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PLATE VII 

TRANS. AM. SOC. CIV. ENG'RS. 

VOL. XXII- N? 431 • 



WESTON 

O N 

FLOW OF WATER IN PIPES 



J^ia&rciTTttTVb. 7 . 




t cUrt z,?z<i7z&sr. 



PLATE VIII. 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 4-31 



WESTON 

O N 

FLOW OFWATER IN PIPES 



3)uzff7-a,7?t, <7Va, <$ . 




■f <Z zaz t?co?te^. 



PLATE IX. 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTO N 

O N 

FLOW OF WATER IN PIPES 



JDiagrraTTis JVb. 9. 



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PLATE X 
TRANS. AM. SOC. CIV. EING'RS. 
VOL. XXII. IN? 431 



WESTON 

O N 

FLOW OFWATER IN PIPES 



JDiagrGL-ms JYo.lO. 




• • gL i./& z/tofc&s: 



PLATE XI 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. IN? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



JDzezgrroLm, JVb./l. 



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PLATE XII 

TRANS. AM. SOC. CIV. ENG'RS. 

VOL. XXII. N? A3\ . 



WESTON 

O N 

FLOW OF WATER IN PIPES 



rDzjagT-ctTTZs JVb. //C*. 



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PLATE XIII 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 4-31 



WESTON 

O N 

FLOW OF WATER IN PIPES 



jDTUZ{p"Cl77Z, JVh.l<3. 




t & in, zjzck&sr. 



PLATE XIV 
TRANS. AM. SOC. CIV ENG'RS. 
VOL. XXII. N? 431 . 



WESTON 

O N 

FLOW OF WATER IN PIPES 



,2)zja&7*a7?v JVb.14. 








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PLATE XV 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OFWATER IN PIPES 



^xxi^rrcciTt. JVb.JS. 



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PLATE XVt 

TRANS. AM. SOC. CIV. ENG'RS. 

VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



^jDxz^grraTTz- JYa.JG. 




PLATE XVII 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. IN? 431 



WESTO N 

O N 

FLOW OF WATER IN PIPES 



J}z*zx?ra7?z, JVb,jf7. 




PLATE XVIII. 

TRANS. AM. SOC. CIV. ENG'RS. 

VOL. XXII. IN? 431 • 



WESTON 

O N 

FLOW OF WATER IN PIPES 



rZtzjezjgrrttfft, JVb. /&. 



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PLATE XIX 
TRANS.AM.SOC.CIV. ENG'RS. 
VOL. XX!!. N9 431. 



WESTON 

O N 

FLOW OF WATER IN PIPES 



JDtcLgrccm, *7Vb. JO. 




PLATE XX 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



J?iGU7ret7*v JVb.z&O. 



1 



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PLATE XXI 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 43! 



WESTON 

O N 

FLOW OF WATER IN PIPES 



jDz&grrccrrv t7Vb.<&/. 




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PLATE XXII. 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



JJzxJLgrTam, *7Va, &/&. 



90 t7ZC?V. 



■zDctvcy 

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PLATE XXIII. 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



JDzcu?7*a,77t, JV&. £3. 




i 



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PLATE XXIV 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



J~>*xzgrra,7n, JVb.£4. 




PLATE XXV. 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



J)zxu?ra7?i, t7Vcr.£& . 



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■x>9a4t — « — *- 



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+ JDctrcy /.s&y 



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PLATE XXVI 
TRANS. AM. SOC. CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 
O N 
LOW OF WATER IN PIPES 



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PLATE XXVII 
TRANS. AM. SOC.CIV. ENG'RS. 
VOL. XXII. IN? 431 



WESTON 

ON 

FLOW OF WATER IN PIPES 



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PLATE XXVIII 
TRANS. AM. SOC.CIV. ENG'RS. 
VOL. XXII. N? 431 



WESTON 

O N 

FLOW OF WATER IN PIPES 



J9iag7-(i7rz, *7Vb.£<S. 



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3.S 



WESTON ON FLOW OF WATER IN PIPES. 



65 



APPENDIX. 

Loss of Head due to Friction of Water in Pipes having very 
Smooth Interior Sides similar to Brass and Lead Pipes, etc. 

Table calculated from a formula by Edmund B. Weston, M. Am. 
Soc, 0. E., for Pipes 100 Feet in Length, showing: 

1st. The mean velocity of the water flowing in the pipe, in feet per 
second. 

2d. The interior diameter of the pipe. 

3d. The loss of head due to friction, in feet. 

4th. The number of gallons of water delivered per minute. 

Loss of Head due to Friction of Water flowing in Pipes 100 
Feet in length, having very Smooth Interior Sides. 

( Weston's Formula. ) 



■d 

a 
o 
o 


Internal Diameter of Pipe in Inches. 


02 

© 
ft 


y z 


n 


% 


1 


1%. 


© 

© 

a 


1.2 

W '■'-> 


u 
© 

ft©* 


1 & 

© p 


u 
© 

ft© 


1i 


© 
ft ©' 


1.2 

© u 


© 
ft © 


1 2 

© 2 


ft © 


>> 

■+3 




o .2 


^2 
° © a 


00 f- 

8 1 


«-3 . 
°©a 


00 p 

§.2 


<S-2 . 
© a 


oo a 

§.2 


© a 


oo a 

a a 


O 
© 


it 5 O 

8^33 


3§ 
<5 


DO p. 2 




ce 3 ° 
g<o3 


(5 


oo 3 o 

00 Zi ••-< 

g'O-H 


=3* 
o 


oo a o 




> ' 


h! 




p-1 




hJ 




1-1 




h^ 




1 


1.55 


0.61 


1.22 


0.96 


1.00 


1.38 


0.73 


2.45 


0.56 


3.83 


2 


4.94 


1.22 


3.9' 


1.91 


3.21 


2.75 


2.34 


4.90 


1.82 


7.65 


3 


9.85 


1.84 


7.79 


2.87 


6.41 


4.13 


4.68 


7.34 


8.65 


11.48 


4 


16.18 


2.45 


12.79 


3.83 


10.54 


5.51 


7.72 


9.79 


6.02 


16.30 


6 


32.83 


3.67 


25.99 


5.74 


21.43 


8.26 


15.73 


14.69 


12.31 


22.95 


8 


54.57 


4.90 


43.24 


7.65 


35.68 


11.02 


26.23 


19.58 


20.56 


30.60 


10 


81.23 


6.12 


64.39 


9.56 


' 53.17 


13.77 


39.14 


24.48 


30.72 


38.25 


13 


130.17 


7.96 


103.26 


12.43 


85.32 


17.90 


62.90 


31.82 


49.44 


49.73 


16 


189.61) 


9.79 


150 . 49 


15.30 


124.41 


22.03 


91.82 


39.17 


72.26 


61.20 


20 


284.81 


12.24 


226.19 


19.13 


187.10 


27.54 


138.24 


48.96 


108.92 


76.60 


25 


429.08 


15.30 


340 93 


23.91 


282.17 


34.43 


208.71 


61.20 


164.64 


95.63 


30 


600.90 


18.36 


477.65 


28.69 


395.48 


41.31 


292.79 


73.44 


231.16 


114.75 


35 


799.95 


21.42 


636.09 


33.47 


526 84 


48.20 


390.32 


85.6s 


308.39 


133.88 


40 


1026. 


24.48 


816.02 


38.26 


676.08 


55.08 


501.16 


97.92 


396.21 


163.00 


45 


1279. 


27.54 


1017. 


43.04 


843.03 


61.97 


625.23 


110.16 


494.54 


172.13 


50 


1558. 


30.60 


1240. 


47.82 


1028. 


68.85 


762.44 


122.40 


603.35 


191.26 


55 


1863. 


33.66 


1483. 


52.60 


1230. 


75.74 


912.71 


134.84 


722.58 


210.38 


SO 


2195. 


36.72 


1748. 


57.38 


1449. 


82.62 


1076. 


146.88 


852.11 


229.50 


65 


2553. 


39.78 


2033. 


62.17 


1686. 


89.51 


1252. 


159.12 


992 01 


248.63 



66 



DISCUSSION OK FLOW OF WATER IN PIPES. 



Loes of Head due to Fbiction of Watek flowing in Pipes 100 feet 

IN LENGTH HAVING VEEY SMOOTH IntEBIOB SlDES. 

(Weston's Formula.) 



9 






Internal 


Diameter of Pipe in Inches. 






02 

u 

05 
ft 


IVz 


2 




2 


> 
2 


3 


- 


■2 


Velocity in Feel 


"S 6 

0-* • 
o> 9 

CC 3 O 

§■*£ 

hi 

0.46 


u 
ft <J 

03 3 

9 


"Si 

05 9 2 

hi 


r-< 

0) 

•ft <u 

CO 3 

8 9 
"ei ^ 


1! 

SH O 

a> 9 
DO 9 2 

hi 


r-i 

ft aJ 
w 2 
° 9 

"3 ^ 
15.30 


1« 

TO .rl 

05 9 

00 B C 

hi 


u 

03 

ft qj 

os 9 

§.s 




1.2 

£ <~ 

<H O 
O -^ ■ 

ao 2 g 

03 9 2 


u 

GS 

ftd 

03 B 

B 9 
c .3 

"to " 


1 


5.51 


0.32 


9.79 


0.24 


0.18 


22.03 


0.14 


30.00 


2 


1.47 


11.02 


1.04 


19.58 


0.78 


30.60 


0.60 


44.06 


0.48 


60.00 


3 


2.96 


16.52 


2.10 


29.38 


1.58 


45.90 


1.24 


66.10 


0.99 


90.00 


4 


4.89 


22.03 


3.48 


39.17 


2.64 


61.20 


2.07 


88.13 


1.67 


120.00 


6 


10.03 


33.05 


7.18 


58.75 


5.47 


91.80 


4.33 


132.19 


3.51 


180.00 


8 


16.78 


44.06 


12.06 


78.34 


9.23 


122.40 


7.34 


176.26 


5.99 


240.00 


10 


25.11 


55.08 


18.09 


97.92 


13. «9 


153.00 


11.08 


220.32 


9.08 


300.00 


13 


40.47 


71 . 60 


29.26 


127.30 


22.54 


198.90 


18.05 


286 . 42 


14.85 


390.00 


16 


59.22 


►8.13 


42.92 


156.67 


33.14 


244.80 


26.63 


352.51 


21.97 


480.00 


20 


89.38 110.16 


64.95 


195.84 


50.29 


306.00 


40.52 


440.64 


33.54 


600. CO 


25 


135.25 


137.70 


98.53 


244.80 


76.49 


382.50 


61.80 


550.80 


51.30 


750.00 


30 


190.08 


165.24 


138.73 


293.76 


107.92 


459.00 


b7.38 


660.96 


72.71 


900 00 


35 


253.77 


192.78 


185 50 


342.72 


144.54 


535.50 


117.23 


771.12 


97.72 


1050.00 


40 


326.24 


220.32 


238.78 


391.68 


186.31 


612.00 


151.32 


881.28 


126.33 


1200.00 


45 


407.44 


247.86 


298.54 


440.64 


233.20 


688.50 


189.64 


991.44 


158.53 


1350.00 


50 


497.30 


275.40 


3H4.73 


489.60 


285.19 


765.00 


232.15 


1101.60 


194.28 


1500.00 


55 


595.79 1 


3d2.94 


437.33 


538.56 


342.26 


841.50 


278.87 


1211.76 


233.60 


1650.00 


60 


702 87 


330.48 


516.31 


: 87.52, 


404.38 


918.00 


329.76 


1321.92 


276.46 


1800.00 


65 


818.51 

i 


358.02 


601.66 


636.48 


471.55 


991.50 


384.82 


1432.08 


322.86 


1950.00 



DISCUSSION. 



Rudolph Heeing, M. Am. Soc. C. E. — The present paper, like the 
former ones of Mr. Weston, contains matter of considerable value and 
interest and bears testimony to the painstaking and the accuracy in de- 
tails "with which its author has approached the problem. The com- 
pleteness with which most of the known experiments on the flow of 
water in pipes have been given and arranged is, I think, not exceeded in 
any other single publication. The new formula which he has devel- 
oped therefrom for the flow in very smooth pipes of \ to Z\ inches in 
diameter is, as he clearly demonstrates, practically correct, and is pos- 
sibly the best one that has up to the present time been suggested within 
the limits and under the qualifications given. 

My object in sending this discussion is not to question the accuracy 
of this formula, but to express my doubts as to the propriety of advocat- 
ing one having what I think is a faulty construction. Had the author 



DISCUSSION ON" FLOW OF WATER IN" PIPES. G7 

•confined himself to recommending the table on page 55, which gives 
the values of the co-efficient of friction within the indicated limits of the 
diameter of pipe and of the velocity in the same, or had he recommended 
a diagram exhibiting these values, I should have said that I believe the 
table or diagram gives the most reliable published average results for 
the purpose set forth in its heading. To suggest a new formula, how- 
ever, particularly with so limited a range of applicability as in this case, 
is, I think, somewhat questionable wisdom. It is a case similar to that 
mentioned by Mr. F. P. Stearns, M. Am. Soc. C. E., in the discussion 
of Yonge's formula (see Transactions, Am. Soc. C. E., Volume XIY, 
page 15), which if applied not far outside of a given range may lead 
far from the truth. Could we always append to the formula the limits 
of its range as readily as we can indicate them in the integral calculus, 
this objection to the formula would not hold good. But as a rule this 
is not done, and we find one book after another, or one engineer after 
another, quoting formulas, but stripped of some of their essential 
qualifications, and then using them for what they were never intended. 
By naturally fixing the limitations in the form of tables or diagrams no 
one could unsuspectingly drop into an error. 

Further, I am not able to agree with Mr. Weston on the fundamen- 
tal construction of his formula. He has followed the precepts of Darcy 
in recommending a separate and distinct mathematical expression for 
different degrees of roughness of the interior surface, whereas we ob- 
serve as much and even more continuity in its variation, as it changes 
from the smoothness of glass to the roughness of old cast-iron pipe, than 
we observe in the diameter of marketable pipes, and therefore might, 
with almost equal propriety, deduce a separate formula for each diam- 
eter. In fact, we see that often a barely appreciable difference in the 
character of the interior surface has a greater effect upon the co-efficient 
than a measurable difference of diameter. 

It therefore seems to me essential to the proper construction of any 
formula used for the flow of water in pipes, that the degree of rough- 
ness should be embodied in it as a variable and determinable quantity 
just as much as the diameter, the leugth of pipe, or its hydraulic gra- 
dient. The introduction of such a variable, as is well known, was first 
attempted by Messrs. Ganguillet and Kutter. While I am convinced that 
their own formula can be improved both in construction and in the nu- 
merical values of its constants, yet it seems indisputable that the sug- 
gestion of a variable co-efficient of roughness is a step in advance which 
I think should no longer be ignored. Such a co-efficient gives the en- 
gineer an opportunity to exercise practical judgment in the selection of 
a definite value for it in accordance with the nature of the perimeter, 
which he is incapable of doing intelligently with a formula in which 
the co-efficient represents the combined effects of a number of causes, 
and conceals the separate effect of each one of them. 



68 DISCUSSION ON FLOW OF WATER IN PIPES. 

Nor do I think it logical, by following Weisbach's lead, to base the 
variation of the only co-efficient upon the velocity rather than upon the 
gradient or slope which produces it. There are good reasons for not 
doing this in large rivers where the slope is often inconsistent with the 
velocity, or cannot be determined with equal accuracy. But for pipe 
systems, where the hydraulic gradient can so readily be measured, I 
think formulas ought to have their co-efficient based upon the slope, 
irrespective of the other inconvenience in Weisbach's method of being 
first obliged to approximate the desired velocity in order to find the 
proper coefficient. 

That Mr. Weston could not obtain a satisfactory formula for old cast- 
iron pipes is due to the fact that virtually he was trying to find for them 
a fixed degree of roughness. Had he introduced a coefficient per- 
mitting the exercise of some judgment regarding the relative degree of 
this roughness in a particular pipe, he would, I think, have found a for- 
mula in which he could have had more confidence. 

Edmund B. Weston, M. Am. Soc. C. E. — I regret that I have not 
been able to construct a formula for the flow of water in pipes having 
very smooth interior sides, similar to lead and brass pipes, which I can 
recommend for larger diameters than 3.5 inches ; but unfortunately I 
had not sufficient experimental data to do this satisfactorily. I there- 
fore restricted myself to the experimental data that I had at hand, and 
constructed a formula which agrees remarkably well with experimental 
results, as can be seen by examining the diagrams from No. 7 to No. 14. 
I was well aware that there would be a possibility of the formula being 
applied to pipes having larger diameters than 3.5 inches, consequently 
I was very particular in my paper to emphasize, in addition to the limit 
of diameters, the nature of the pipe for which the formula was intended. 
And as the pipes whose interior sides are very smooth, which have diam- 
eters larger than 3.5 inches, are not used at the present time to con- 
vey water, unless possibly in very exceptional cases, it seems to me that 
with reasonable precautions there should not be any danger of the 
formula being applied beyond its limit. In fact there are few formulas 
but what are in reality more or less limited in their range, if the experi- 
ments from which they were constructed are criterions; even Ganguillet 
and Kutter state that their formula must not be expected to apply to 
cases beyond the range of the data from which it was derived. 

I recognize how valuable a reliable general formula would be which 
could be applied to all kinds of pipes, and which would contain a 
co-efficient permitting the exercise of some judgment regarding the 
relative degree of roughness in a particular pipe ; but had I been dis- 
posed to have attempted the construction of such a formula, it would 
not have been possible for me to have done so from the experimental 
data that I had accumulated, as a preliminary investigation that I 



DISCUSSION ON FLOW OF WATER IN" PIPES. 69 

made relative to a formula of this kind developed results from these 
data which were entirely too conflicting. 

• Mr. Hering's opinion that formulas ought to have their co-efficients 
based upon the hydraulic gradient rather than the velocity, does not 
entirely coincide with my views in regard to formulas for the flow of 
water in pipes under pressure, although I admit that such formulas 
would be very convenient at times, as in the majority of cases in water- 
pipe calculations the result sought after is the loss of head due to fric- 
tion, and not the velocity, as is generally the case in calculations relating 
to rivers and open channels. 

In regard to constructing a perfect and reliable ganeral formula that 
could be applied to old cast-iron pipes, if such a thing were possible, 
especially if the age of the pipes was the basis upon which judgment 
was to be formed as to the condition of their interior surfaces, it seems 
to me that in addition to a co-efficient of roughness, etc., etc., it would 
be quite important to embody in the formula a co-efficient dependent 
upon the chemical constituents of the water that was flowing in the 
pipes, or that was to flow in the same, as it is well known that some 
waters cause cast-iron pipes to corrode much faster than other waters. 
For instance, it can be seen in Table No. 1 that co-efficients of friction (£) 
worked out from experiments that were made in Philadelphia with cast- 
iron pipes respectively seven and eleven years old, are about twice as 
large as co-efficients of friction (£) derived from experiments that were 
made in England with cast-iron pipes respectively seven and thirteen 
years old. 

Chas. E. Emery, M. Am. Soc. C. E. — I had occasion to closely 
examine the general formulas on the subject of the flow of fluids in de- 
veloping an expression for the flow of steam. The formula selected 
was based on that of Weisbach, and the simple form applicable for 
water was found to answer every purpose for small losses of pressure in 
transmission, although a differential formula was developed to cover all 
conditions. In a cursory examination of the various papers that have 
been read on the subject of the flow of water, it has occurred to me 
that the consideration of one important source of information has been 
omitted. Experiments have been made with great care on the skin 
resistance of vessels moving through the water. Froude published, in 
the Transactions of the British Association for the Advancement of 
Science, some ten years ago, a series of curves showing the resistance of 
a large model hull at different velocities and for different lengths of sur- 
face operated upon. He found that the unit resistance decreased rapidly 
as the length was increased, but became nearly constant after the length 
exceeded 100 feet. Necessarily the frictional resistance, caused by the 
interior surface of pipes, corresponds to the skin resistance of a vessel 
in the water, and the results from the two methods of experiment can 



70 DISCUSSION ON FLOW OF WATER IN PIPES. 

be compared with advantage. The Froude results show that experi- 
ments with short pipes should show greater resistance. 

I fully agree with Mr. Hering that all the results of experiments 
should be shown by one general formula. This can only be accomplished 
by introducing in such formula a suitable number of variables, usually 
called constants, which can be modified to suit the particular conditions 
and thereby cause the formula to produce substantially the experimental 
results. It has been stated again and again that the character of the 
interior surface should be considered in the formula, but it does not as 
yet appear to have been done satisfactorily. I have heard the proposed 
constant termed the co-efficient of rugosity, although the term does not 
appear in either of the papers of the Society. The skin resistance has 
been pretty well shown to be due to eddies produced by the roughness 
of the surface. Old navigators can tell pretty well the speed of a vessel 
by looking at the distance the foam produced by the eddies extends 
from the side. In a running stream the water striking large stones be- 
low is thrown upward to the surface, as shown clearly by Mr. Francis* 
experiments with white-wash in one of the races at Lowell. In a dis- 
cussion of that paper I called attention to how well these experiments 
compared with the accepted theories of eddy resistance. The rougher 
the surface the more the particles are deflected from a direct course and 
the farther the eddy resistance penetrates the central stream. It would 
seem that sufficient experiments are now available with surfaces of 
different characters to enable a co-efficient to be introduced into the 
ordinary water formula which would allow accurately for all customary 
variations. It might be well for those interested in the subject to 
examine some discussions by Rankin and others on the laws of eddy 
resistance, so that the co-efficient of rugosity would be introduced at 
the proper power to produce variations corresponding with those shown 
by experiment. 

Mr. Weston. — D'Aubuisson in his " Traite D'Hydraulique," pub- 
lished, I think, about 1850, in an article upon the action of water by 
its resistance, recognizes that the increase in the length of a body 
moving through the water very perceivably diminishes its unit of re- 
sistance. 

A few preliminary experiments that I made in 1876, relative to the 
flow of water in pipes, owing to the peculiarity of the results obtained^ 
led me to make an investigation with the experimental data of quite 
a number of authorities in order to ascertain if the co-efficient of 
friction (£) was in any way dependent upon the length of the pipes. 
This investigation was rather an unsatisfactory one in some respects, as 
in nearly the whole of the experimental data of the very short pipes 
that were used the co-efficient of influx ( e) entered into the problem, and 
in some instances it had to be assumed. The results, however, showed 



DISCUSSION ON" FLOW OF WATER IN" PIPES. 71 

decidedly that the value of the co-efficient of friction (£) was not in- 
fluenced by the length of the pipes. 

1 1 have already expressed my views in]regard to a general formula in 
my reply to Mr. Hering's discussion. 

E. Sherman Gould, M. Am. Soc. C. E.— This paper contains the 
results of some interesting experiments upon the flow of water in pipes, 
as well as a very comprehensive and valuable review of the labors of 
other investigators in the same line. 

The great number of these experiments which have been made, and 
the somewhat discordant formulas deduced from them, naturally lead us 
to inquire into the cause of such disagreement. 

This much must be said of all formulas founded upon experiment : 
granting the accuracy of the measurements and records, the formulas 
must be true for the cases from which they were derived, and any others 
which should give different results would, for these particular cases, be 
incorrect, for the results were known in advance, and the formulas made 
to fit them. 

The value of such formulas depends wholly upon the extent, perfec- 
tion and trustworthiness of their experimental data. In these respects 
the magnificent researches of Darcy seem to command the greatest 
confidence. No other experiments, unless conducted upon a still more 
perfect scale and guided by a surer and more discriminating judgment 
than his, should be considered as invalidating the results left us by this 
illustrious experimentalist. So far from being invalidated, it would 
appear that his formulas have been generally corroborated by subse- 
quent investigations. Mr. Charles B. Brush's observations on a 20-inch 
main, which have been already laid before the Society, and quoted in 
this jDaper, agreed very closely with those obtained by using Darcy's 
formulas for the same data. Darcy's experiments do not include the 
larger diameters of pipe, but I understand that the actual volumes dis- 
charged by the 48-inch main of the Bronx Eiver Water Supply agree 
within three per cent, of those given by his formula. I am glad to 
perceive, by the paper now under discussion, that Mr. Weston also finds 
his results to agree very well with those of Darcy. 

From a practical point of view, the state of the question seems to be 
this : Given a certain number of trustworthy experiments it is easy to 
formulate an equation which shall return the observed results, and this 
equation will always be true for identical conditions of pipe. But any 
change in the conditions will vitiate the formula to a greater or less 
extent, and render a new one necessary. In order to apply the formula, 
we must know exactly the conditions upon which it was framed. These 
can only be described by saying that the interior surface of the pipe was 
"smooth," or "rough," or "slightly tuberculated," etc. All this is 
very vague, and yet the state of the inside surface is a controlling factor 
in the problem. Moreover, a system of pipes when first laid is, or 



72 DISCUSSION" ON" FLOW OP WATER IN PIPES. 

should be, in a condition of smoothness. Later, it will become more or 
less rough or even tuberculated, which will not only change the char- 
acter of the inside surface, but also reduce the diameter. It would 
seem idle, therefore, to go into a great refinement in the matter of a 
formula, particularly if the refinement leads to a shaving down of the 
diameter. 

As regards the effect of the velocity itself as affecting the formula, 
although there seems to be no doubt that the co-efficient for the same 
pipe varies somewhat with the velocity — that is, with the sine of the angle 
of inclination — yet, it must be remembered that in practice no very 
great extremes of velocity, either way, are admissible, so that this 
factor is kept within comparatively narrow limits of variation, admit- 
ting of a mean value being assumed, for most cases. 

I would not be understood as depreciating the value of such 
researches as those embodied in Mr. Weston's able and instructive paper. 
They lie at the very foundation of all sound science. I would wish 
simply to direct attention to the immediate bearing of the formulated 
results upon the actual practice of designing a line of water supply pipes, 
and to indicate what we can and what we cannot expect from a formula 
in this connection. 

Mr. Weston. — That Mr. Gould has such a high opinion of the value 
of the investigation and formulas of the late Henry Darcy, I am very 
glad to learn, not only on account of my having recommended his for- 
mulas for new cast-iron pipes, but for the reason that a number of writers 
upon hydraulic subjects have seemingly taken great pains not only to 
depreciate the formulas of this eminent engineer, but also to question 
the value of his experimental results. I regret, however, that Mr. Darcy 
did not deduce a formula for pipes having very smooth interior sides, 
although his experiments with pipes of this class were somewhat 
limited. 

Mansfield Meekiman, M. Am. Soc. C. E. — The formula deduced by 
Mr. Weston for loss of head in friction has the disadvantage, in com- 
mon with those presented by other authors, of being empirical and not 
rational. It is not easy to see, however, how a theoretical expression 
for this lost head can be established, and accordingly experiment must 
be the only guide for a long time to come. Mr. Weston's formula can 
be written thus: 

8. ji 

h F = 0.0126 -J-. 4- + 0.0315 —-. £ 0.06 I ^~ 

J d 2g d 2g 2g 

in which only the first term of the second member is homogeneous with 
Tip indicating that the numbers 0.0315 and 0.06 are functions of v or d, 
whose relations are not yet known. I do not like the presence of the 
minus sign before the last term of this expression, for if the friction head 
be due to several carses it is not easy to see why any cause would pro- 
duce a negative effect. 



DISCUSSION" ON" FLOW OF WATER IN PIPES. 73 

The diagrams show that the formula agrees very well with the experi- 
ments, and hence the labors of Mr. Weston will be of value to all who 
wish to make computations on the discharge through pipes. It is my 
impression that other formulas might be devised which would exhibit 
an accordance nearly or quite as good, but it does not seem very impor- 
tant that further investigations should be undertaken until something 
is known regarding the theoretical laws which control the friction of 
flowing water. With such a complex empirical expression as that of 
Kutter's formula I have no sympathy whatever. The laws of nature 
are, of course, not simple, but it cannot be at all supposed that the true 
law of loss of energy in friction is represented by such algebra as 
Kutter's formula contains. 

The loss of head due to sudden contraction of the diameter of a pipe 
is, I think, always less than that given by Mr. Weston. He states for 
all cases that the co-efficient is 0.316, and that this is increased by 
resistance and friction to 0.505. Now the number 0.505 applies to the 
case where the diameter d (Fig. 4),* is very large compared with cf,, as 
for instance, when water enters a pipe from a reservoir. It is clear that 
when d = c? lt the value of should be zero, for in this event no loss of 
head due to contraction occurs. A proper expression for the value of 
should hence depend upon the ratio of rf to rf 1( As a reasonable 
approximation I suggest the formula: 



<P 



-*(?-*> 



in which c 1 is the co-efficient of contraction of the stream in passing 
through the orifice whose diameter is d lt Let r denote the ratio of d to 
di, then the value of c 1 in terms of r may be stated by the following 
expression, proposed in the second edition of my Treatise on Hy- 
draulics : 

. = 0.582 + ££= 
1.1 — r 

which is based upon the mean value c 1 =0.62 when r = 0, and the 
known result c 1 = 1.0 when r = 1. The numerical values of for dif- 
ferent values of r can now be ascertained, c 1 being first computed, and 
thus are found, 

For r = 0.0, 0.2, 0.4, 0.6, 0.7, 0.8, 0.9, 1.0. 
= 0.50, 0.47, 0.42, 0.34, 0.28, 0.20, 0.09, 0.00. 
These values of <p are given with only two decimals, for I regard it 
as useless to write the third decimal in cases where even the second is 
uncertain. 

Mr. Weston.— I consider the ideas of Professor Merriman relative to 
the co-efficient of resistance (0) of water passing from a large to a small 
pipe very reasonable. I gave in my paper, as I so stated, the co-efficient 

*d and d L being diameters, and F and F t areas, as indicated on Fig. i, page 62. 



74 DISCUSSION" ON FLOW OF WATER IN PIPES. 

of Weisbach, as I had not made any experimental investigation based 

upon the idea of determining a co-efficient of this kind, considering that 

his co-efficient was a safe and simple one to use. The difference, how- 

v 2 
ever, in the loss of head by the formula hf= (p-^~, would be only 0.11 

9 . 

feet for the greatest velocity that water should be allowed to flow 

through distribution pipes, by using either the smallest co-efficient 

0.09 given by Professor Merriman, or the co-efficient 0.505 of Weisbach. 

I have found recently in the second volume of Weisbach's work that 

/ F x \ 2 
a formula corresponding to = I 1 jt- ) is mentioned (the co-effi- 
cient given in my paper being taken from the first volume). 

John B. Freeman, M. Am. Soc. C. E. — The present state of the art 
of computing the loss of head in an ordinary given pipe when delivering 
a given quantity, is about like figuring out a formula to four places of 
decimals and getting a result that may be relied upon as correct within 
25 per cent. We are all interested in efforts to reduce this margin of 
uncertainty. 

Occasional reports of Mr. Weston's work in the field of water supply 
have given me full confidence in the earnestness with which he seeks the 
truth and have led me to respect the generous diligence with which he 
gives the results of his labors to the craft. 

I feel more free to discuss the matter at this time from the fact that 
the author has full opportunity to reply to all comments and criticisms 
in closing the discussion, and believe it for the best interests of both 
the Society and the authors that all papers like this should be subject 
to a searching examination from the different points of view of different 
minds while the whole matter is fresh and the author has opportunity to 
answer and explain. 

It seems to me that Mr. Weston is off the true road towards a thor- 
oughly satisfactory formula for the flow of water in pipes. 

I would maintain as a foundation principle that a formula represent- 
ing the law of flow in pipes, to be satisfactory, must contain as a very 
important and controlling factor, a term dependent upon the roughness 
of the interior surface of the pipe. 

Mr. Weston's discussion of this question does this only in a crude 
and indirect manner, by adapting special formulas, each of narrow appli- 
cation, to some of the different classes of pipes. In one case his variable 
co-efficient is a function of only the diameter as a variable, in another of 
only the velocity, and in another of both the diameter and the velocity. 

There is no reason to suppose that the actual law thus varies. 

His investigation brings but little new data to light, and thus is not 
an experimental but an algebraic research, seeking the equation to a 
curve, which shall be as nearly as possible the mean of the plotted data 



DISCUSSION ON FLOW OF WATER IN PIPES. 75 

for each of the several classes into which he divides certain data already 
well known and discussed. 

Mr. Weston's form of investigation does not seek an expression for 
a law that is broad and general and covers the flow in all pipes, and in 
fairness to him we must, I think, admit that there is not on record the 
data with which he could have conveniently sought one. 

I believe there is such a law, and that when we have more experi- 
ments it will be found. The missing link now needed to tie experiments 
on different pipes together and bring them exactly into one line, or ex- 
plain the discrepancies in our data such as are so well shown in the con- 
venient diagrams appended to Mr. Weston's paper, is an accurate and 
strictly definite description of the character of the surface. 

It is surprising how this part of the description has been neglected 
in nearly all recorded experiments relating to the friction loss in iron 
pipes. Take even Darcy's experiments, in which he demonstrated what 
Hamilton Smith, Jr. calls the most brilliant hydraulic discovery of the 
century — the powerful influence of character of surface on the flow. 
The part of this research relating to effect of rough deposits was a quali- 
tative analysis and not a quantitative analysis, for where, in his memoir, 
can you find it stated whether the tubercles or deposits which he found 
to double the friction loss were on an average as large as grains of 
wheat, or as large as cherries ? This is important information to have, 
since it might correspond to 50 per cent, or more difference in the loss 
of head. 

While discussing the desirability of including a special co-efficient of 
roughness in our future formula, we may refer to the fact that that equa- 
tion of wonderful range, the " Kutter formula," is applicable to express 
the law of flow in pipes, and that it contains a special co-efficient of 
roughness, and that in the very complete and convenient table of 
hydraulic data, given by Messrs. Hering and Trautwine in their appen- 
dix to Ganguillet and Kutter's treatise,* published about a year ago, 
nearly all of the five hundred experiments tabulated and described by 
Mr. Weston are there presented with the Kutter co-efficient of rough- 
ness computed for each. 

This effort to describe the law of flow in all pipes by a single equa- 
tion is highly commendable from a broad, general point of view, but it 
is not, however, altogether satisfactory. 

I am inclined to think that some far simpler equation than that of the 
Kutter co-efficient may be found, which will express the law of flow in 
pipes so accurately that the error coming from approximations involved 
in its algebraic form will be le s than the actual variations in flow due 
to differences of roughness so small as to be altogether inappreciable in 
any ordinary description in character of surface. 



* Flow of Water in Rivers and other Channels.- Wiley & Sons. New York, 18d9. 



76 DISCUSSION" ON" FLOW OF WATER IN PIPES. 

Turning, now, to the subject of loss of head in clean and new cast- 
iron pipes : These by no means all have the same character, and it is 
useless to expect one formula with one constant to apply to all. Thus, 
for instance, we, perhaps, explain in part the difference of 25 per cent, 
in co-efficient C found between Darcy's results and the two newly 
reported experiments of Mr. Weston on a 6-inch pipe. I have seen dif- 
ferent lots of new 6-inch cast-iron pipe, which differed so much in 
character of surface that I have little doubt but the loss of head would 
be considerably more than 25 per cent, greater in one than in another. 
This difference in surface came from the degree of skill with which the 
tar coating was applied even more than from the difference in the cast- 
ing as it came from the foundry sand. Thus some tar-coated cast-iron 
pipe is very smooth on the inside, while other pipe has " ribs " of tar 
projecting about -jpg-inch, or even j-inch, running part way around the 
circumference where the tar has run while soft. On studying the col- 
lection of experiments on new cast-iron pipe now available as data and 
transcribed from one book to another, and given with fullness in Iben's, 
Smith's, Hering and Trautwine's and Weston's discussions, it will be seen 
that causes like this can easily obscure the true law or the refinements of 
a complicated formula. 

Until we have new experiments on pipes in which great care is taken 
to accurately and definitely describe the exact degree of smoothness of 
the interior surface, it is almost hopeless to try and derive an accurate 
general formula. Meanwhile, had we not best try earnestly to avoid 
complicated algebraic expressions, and keep our formulas in the simplest 
possible form. 

In other words, is not that simple formula of the last century, the 
Chezy formula, so called, when accompanied by a short and simple table 
or diagram of values for its co-efficient, better for practical use than any 
of the more complicated formulas? Until we get that extended series of 
quantitative experiments on effect of roughness is not this simple Chezy 
formula : V= G V K S. 

In which V = velocity in feet per second. 

C = co-efficient of flow dependent on diameter, velocity 

and roughness (Smith represents this by 2V). 
R = hydraulic radius = £ diameter of pipes of circular 

section. 
8 = slope = ratio of loss of head to length of pipe, 

the best framework on which to display for comparison such new bits of 
experimental data as we may from time to time secure. Hamilton 
Smith, Jr., so used it in his most excellent treatise* (which is, perhaps, 
the most thorough of all in the care taken to exclude questionable data) ; 
and so did Hering and Trautwine in the appendix to their excellent 

* Hydraulics, Hamilton Smith, Jr. Wiley & Sons. New York, 1886. 



DISCUSSION ON FLOW OF WATER IN PIFES. 77 

translation of the Ganguillet and Kutter work, given to the profession a 
year ago. 

The valuable tables of data in the two recent books just mentioned 
give nearly all the experiments on flow in pipes recorded for a hundred 
years back, which have value as data and include nearly all those pre- 
sented by Mr. Weston. When presenting new data by reducing it to 
this form, it is much more convenient for reference and comparison. 

For the present, is it not better to observe experiment and secure 
new co-efficients for the old formula rather than re-thrash old, and in 
many cases blighted straw, to devise a new formula? 

With regard to very rough or corroded pipes, Mr. Weston, like 
nearly every author who attempts to devise special formulas for the 
experiments now on record, or attempts to make experiments on one 
pipe fall in line with those on another, finally gives it up as a bad job. 

The trouble in reconciling the experiments is, I think, in general, 
not that the loss of head has been inaccurately measured, not that the 
delivery was improperly determined, nor is it that the net diameter is 
not precisely known. 

The uncertainty comes from vagueness in describing the character of 
the surface. The exact character of the surface is not easy to deter- 
mine. In many cases there is no opportunity to inspect it, and even if 
opened to inspection a corroded surface is difficult to describe with 
precision. 

In the present state of our experimental knowledge is it not almost 
useless to attempt a special form of equation for these very rough pipes? 
Is it not better to arrange the results of such experiments in the form of 
a comparison of the loss of head found in the rough jripe with that 
deduced from our simple formula for an average ordinarily smooth 
pipe, and thus, for instance, say that in the case of a certain pipe 
corroded as described, it was found that the loss of pressure was 2.4 
times as great as the formula shows for a smooth pipe of same size and 
with same delivery? With each experiment expressed in this way, but 
condensed into tabular form along with the various hydraulic elements 
of the case, the present data is in most convenient shape for practical 
application, and is of very great value in conspicuously calling attention 
to the danger when designing works of computing the friction loss as 
though the pipes were always to remain new and clean. 

With regard to the particular style for the fundamental formulas, I 
notice that Mr. Weston, on page 6 of his paper, presents the formulas 
which his own experience has shown most convenient. These are those 
sometimes known as Professor Weisbach's.* Is not the convenience of 
this type, as compared with the modified Chezy form as used by Smith, 
Hering and Trautwine and others, a question of personal habit more 

* Cox's Translation Weisbach's Mechanics, page 866 and page 870. Van Nostrand, 1872. 



78 DISCUSSION ON FLOW OF WATFE IN PIPES. 



than anything else? The latter formulas include the value of j/ 2 g 
in its constant, and thus gain slightly in simplicity. I was interested 
a while ago to look up this matter and see how much accuracy it was 
possible to lose in so doing. 

If for the value of V 2 a we always use 8. 02, the greatest possible error 
that it will involve for any place in latitudes anywhere between the 
southern point of Greenland and Key West, and anywhere from sea level 
to 5 000 feet elevation will not be more than one-tenth of 1 per cent. 

Thus, proj)er as it may seem to keep this value in sight in a general 
formula for text-book use, it seems needless to load a practical formula 
down with it, and we are justified in incorporating merely its aveiage 
value into the constant of our formula for ready practical use where 
differences of surface so small they can hardly be noticed may cause 5 
per cent, difference in the friction loss.* 

On pages 6 and 7 of Mr. Weston's paper certain special formulas are 
presented for compound pipes and branching pipes. These are presented 
for practical use, and Mr. Weston uses their derivation as an argument 
for preferring the Weisbach arrangement of formula. On looking into 
these with a little care it appears that the formulas are less simple in 
their application than would appear from the first glance, since w T hen 
seeking v for a given h in problem No. 5, for instance, the several values 
of C all depend on v, and the problem can therefore be solved only by 
successive approximations. Second, it seems to me that problem No. 5 
especially presents a symmetry in the equal size and length of the pipes 
in the successive subdivisions, which would almost never occur in ordi- 
nary practice, and therefore I do not think the facility in deriving these 
formulas should be allowed to weigh too heavily in favor of the Weis- 
bach form. 

On pages 62 and 63 Mr. Weston copies from Weisbach without 
change or comment some formulas for effect of curves, which, though 
sad to tell, are the best yet on record, were derived from very small 
pipes, and may with good reason be distrusted, and ought not to be 
quoted in this manner without some limit or qualifications. 

It may be noted that at the middle of page 62 the formula for effect 
of contraction as it stands is without meaning. A proper form is 

<p = ( lj in which c is co-efficient of contraction which depends 

on the relative area Of F x and F, and thus needs a table of values to 
accompany the formula. 

In other words, the formula as printed implies that <p is a constant 
whatever the amount, of reduction in diameter; whereas, from the 
nature of the case, it must be a variable of considerable range. 

* We might, indeed, in the effort to get things iuto the most convenient shape for 
practical use waive even a little more of the theoretical shape and write Q = c' */ d b h m 



DISCUSSION ON FLOW OF WATER IN PIPES. 79 

With regard to the table of data and descriptions, occupying from the 
8th to the 48th page, it appears that the experiments on two of the pipes 
there mentioned are original and published for the first time. Nearly 
all the others, which are reliable enough to found a formula upon, have 
been discussed in what seems to me a more thorough and searching 
manner by a distinguished member of our Society, Mr. Hamilton Smith, 
Jr., in his book published three years ago, and, as already intimated, all 
have their hydraulic, elements and co-efficients adapted for both the 
Kutter and the Ohezy formulas presented in the appendix to Hering 
and Trautwine's translation of Kutter. It is a matter to be regretted 
that the loss of flow deduced by Hamilton Smith, Jr., from substantially 
the same experiments discussed by Weston, was not represented along 
with the other curves upon the very excellent and convenient diagrams 
of Mr. Weston. This, prior to Mr. Weston, was the most recent study 
of the subject,. and although Mr. Smith leaves the subject in rather an 
abrupt and incomplete shape, in that his values for /\ are not clearly 
defined, and that the gaps between his curves of values for practical use 
are rather wide, especially for pipes under 12 inches in diameter — (this 
was influenced, no doubt, by a lack of data, which still exists) — yet, his 
conclusions are of great value. 

Mr. Smith used substantially the same data as that from which Mr. 
Weston satisfied himself that the Darcy formulas were satisfactory, and 
came to a different conclusion and presented a law of his own derivation, 
and one which, like Mr. Weston's new formula for smooth pipes, made 
the value of the co-efficient depend on both the diameter and the 
velocity. It is true Mr. Smith presented his law expressing the values 
of \the co-efficient in graphical form rather than in an algebraic one, with 
perhaps the same view as expressed by a previous speaker, that a curve 
or a table is less liable to be used beyond its proper limits than a 
formula. 

"We may also refer to the very convenient diagram given in Mr. 
J. T. Fanning's comments on Mr. Brush's very interesting paper on 
Waste and Friction Loss in Water Mains,* as another illustration of the 
use of a diagram for expressing the various values for the co-efficient of 
flow in terms of both the diameter and velocity. 

Finally, I may venture the comment that so far as I yet see Mr. 
Weston has left the main question just where he found it ; that is the 
question concerning the flow in ordinary cast-iron pipes, which are those 
that the hydraulic engineer has to deal with in nineteen cases out of 
twenty. As I read the paper through, it seemed that the main new 
feature of value presented is that of the formula for very smooth pipes, 
from i to 3£ inches in diameter. 

The presentation of the experiments by Mr. "Weston upon the 1-inch 

* Transactions, Vol. XIX, No, 395, p. 112, September, 1888. 



80 DISCUSSION ON FLOW OF WATER IK PIPES. 

tin-lined iron pipe and the 6-inch east-iron pipe are to be welcomed ; but 
it is to be regretted that the possible limits of error are not investigated 
and stated, and the experiments described with the fullness so necessary 
to give high scientific value — such, for instance, as that with which Ham- 
ilton Smith, Jr., describes most of the new data on pipes which he pre- 
sented to the Society in 1883, and described in his Hydraulics, page 290 
et seq. As the record now stands we must regard these new experiments 
merely as approximations. 

In the final revision of his paper, I hope Mr. Weston may explain a 
little more fully the magnitude of the obstruction formed by the sheet 
tin bushings at each joint, and will give more fully the method em- 
ployed for determining the loss in the $ tap and in the main from the 
reservoir. 

As to the 6-inch pipe it would add to the value of the experiments if 
Mr. Weston would kindly state the possible limits of error in the fol- 
lowing directions : 

(a.) In general even the best Bourdon gauges are not instruments 
of precision, and scales are liable to unaccountable derangements. 
Were these gauges tested by a mercury column immediately before 
and after the experiments, or was their position reversed ? An error 
of £ pound to each gauge alone might make experiment 325 11 per 
cent, in error. 

(b.) Is it certain piezometer tubes were free of air ? 
(c. ) Were piezometric orifices exactly flush with inner surface and 
normal to axis of pipe ? 

(d.) Was diameter of this particular pipe accurately measured, or 
is the 6 inches the "foundry size ?" 

(e. ) This pipe apparently was not laid with a view to the experi- 
ments or inspected after them. Is it absolutely certain it contained 
no obstruction like a bunch of lead from a bad joint, or that in the 
four years' use no tuberculatum whatever had taken place? 

(/.) Were the lengths of hose the same ones that had been gauged, 
or were they other pieces subject to the ordinary commercial varia- 
tions in diameter and character of surface of different lots ? 
Eternal vigilance and everlasting patience are the price of scientific 
accuracy in this class of work. 

These questions are of interest since Mr. Weston finds a friction loss 
about 20 or 25 per cent, greater than that found by Darcy for the cast- 
iron pipe nearest to this in diameter. Nevertheless, even if these questions 
cannot be answered, and if the experiments are less precise than Mr. 
Weston would have gladly made had circumstances favored, they are of 
value and interest as data, and all such are to be welcomed as a prac- 
tical guide until the longed-for elaborate series of experiments are made 
by a second Darcy. 

The experiments selected by Mr. Weston in developing his formula 



DISCUSSION" ON PLOW OF "WATER IN PIPES. 81 

for smooth pipes are, in some respects, questionable, though undoubt- 
edly they were the best data to be found, and it is no fault of his that 
better data were not in existence. 

Thus: First. — Is it not a little doubtful to use experiments 1 to 14 as 
a basis for a formula, without some statement as to length of pipe and 
conditions under which experiments were made ? Mr. Smith and Messrs. 
Hering and Trautwine exclude these from their table of data. 

Second. — In making use of experiments 28 and 29 by Rennie, upon a 
pipe only 15 feet long, and experiments 59 and 60 by Neville, there is 
liability to error from the fact that in such very short pipes the distribu- 
tion of velocity and regimen of flow is not fully established at upper 
portion of pipe. This may be illustrated by reference to Series III and 
N, page 239, Smith's Hydraulics. Moreover, in each of these cases of 
Rennie's and Neville's experiments, the co-efficient of influx which has 
to be guessed at exercises a proportionally larger influence on the total 
loss of head than for longer pipes. 

Tliird. — For exact scientific purposes it seems hardly fair to class on 
the ground of smoothness experiments on new wrought- iron lap-welded 
gas pipe, f-inch and 1-inch diameter, aloug with the pipes of glass and 
lead. Is it not uncommon for iron pipe to come from the welding fur- 
nace with a skin as smooth as that on a lead pipe as it comes from the 
die? Moreover, why from description alone is it proper to make use of 
Smith's experiments on new uncoated 1-inch gas pipe and reject Darcy's 
experiments on new 1-inch gas pipe, even though results do not agree ? 

Passing to the pipes of larger diameters, quoted by Mr. Weston, if the 
3£-sheet-ironpipe and also the 7.40-inch and the 11. 69-inch of Darcy had 
riveted seams, as stated by Hering and Trautwine, and as seems natural, 
it certainly would give a much greater friction loss than a smooth lead 
pipe, and cannot properly be included. 

It is hardly following *the true scientific method, but is arguing in a 
circle, to include experiment No. 58 by Hodson and No. 237 by Dr. 
Robinson, also Nos. 124 to 139 by Smeaton, as data for determining law 
of flow in very smooth pipes, merely because they hapj3en to coincide 
approximately with the formula, while actually the smoothness of the 
|3ipe is not stated and the kind of pipe or manner of experiment is not 
known, and the diameter given by Mr. Weston to thousandths of an inch 
was apparently merely the nominal or commercial diameter. 

Fourth. — For the tin pipe of experiments 146 to 160 we may ask, in 
order to gain an idea of the smoothness, just what kind of pipe was 
Bossut's " tin " pipe of one hundred years ago? 

Fifth. — It may be of interest to note that the experiments of Leslie 
on 2^-inch lead pipe, No. 250 to 269, and of Provis, on lj-inch lead pipe 
(Nos. 175 to 211), though referred to by Mr. Smith, are by him excluded 
from his results as unreliable. 

Sixth. — Excluding the questionable data, we see that the largesf 



32 DISCUSSION OK FLOW OF WATEE IN PIPES. 

smooth pipe left to furnish data for the new formula is the 2-inch glass 
pipe of Dare j. 

Seventh. — To a person who is experienced in delicate and rigorously 
accurate hydraulic experimentation, the question will often occur, when 
trying to reconcile these early experiments, Did the experimenter clear- 
ly understand the disturbing influence of air bubbles, and were they 
driven out and excluded with positive certainty? 

As we thus carefully examine the quality of the data we see how un- 
satisfactory much of it is as a foundation for a new formula for very 
smooth pipes, and how very few are the really reliable experiments. 

If we wish accurate knowledge of the area of a sharply bounded 
field, is it not better to take a steel tape and a first-class modern transit 
and go out and survey it, making a clean, fresh, first-class job instead 
of hunting among the archives and averaging the more or less rough sur- 
veys of the past hundred years ? 

If, for the time being, Ave desire working knowledge more than ancient 
history, and need accurate and convenient knowledge of the laws of 
flow in very smooth pipes like drawn lead, then if time is money, it 
would cost very little more to have some good lead pipes made I inch, 
\ inch, 1 inch, l£ inch, 2 inch and 3 inch, a hundred feet of each, handle 
it delicately, keep it straight and perfect as it comes from the die, ex- 
periment on it with velocities from \ foot to 25 feet per second, then try 
it bent around certain definite curves, let a plumber coil it up and 
straighten it out two or three times, crook it around half a dozen cor- 
ners and then experiment on it again. 

This is work which could, for instance, be very easily done in the new 
hydraulic laboratory now under construction for the Massachusetts In- 
stitute of Technology, and I sincerely hope it may be undertaken some- 
where and the work done on a suitable scale and under conditions that 
may make the results unquestionable. 

Then with the work once thoroughly well done, the results, with 
their own sharply defined limits, may stand unchallenged for a hundred 
years. 

We all owe thanks to Mr. Weston for the diagrams appended to his 
paper, which show in an extremely convenient and interestiug manner 
the way in which our available data agrees with various standard 
formulas. 

To criticise the investigation or to detract from the just praise due 
Mr. Weston for his industry in presenting these matters is far from my 
purpose. 

The main points I would make are: 

First. — In securing the data now on record far too little attention has 
been paid by experimenters to ascertaining and describing the exact 
degree of smoothness of the wetted surface. 

Second. — Investigators in attempting to derive formulas from the 



DISCUSSION ON FLOW OF WATER IN PIPES. 



83 



data have given too little attention to incorporating in their formulas a 
factor dependent on this roughness. 

Third. — The profession greatly needs a new and extended series 
of experiments before satisfactory general laws or formulas can be 
derived. 

Fourth. — Until we get these it is better to make use of very simple 
and familiar formulas like that of Chezy, and devote our opportunities 
to extending, tabulating and classifying values of the co-efficient. 

In closing I may say that my own experience goes to show that a 
table on the plan of the excellent little table published by George A. 
Ellis, C.E., about ten years ago, but constructed with smaller gaps 
between quantities and diameters, is more convenient for practical use 
than any formulas or the tables in any of the engineering pocket refer- 
ence books. 

The plan of this is as below: 



Gallons discharged 
per minute. 



4-Inch Pipe. 


6-Inch Pipe. 


Mean 
velocity. 
Feet per 
second. 


Loss of 
head per 
100 feet. 


Mean 

velocity. 

Feet per 

second. 


Loss of 
head per 
100 feet. 











Etc. 



If appended to this we could have compiled a table of factors by 
which to multiply these losses of head to allow for different degrees of 
roughness, the whole would be of the utmost convenience, and I hope 
some one who is ready to take his pay in the gratitude of the profession 
will prepare such a table based on some standard investigation. 

Mr. Weston. — I think it is fortunate in many respects that all of the 
members of the human race have not the same opinions, for if such was 
the case, there would be but little I fear to stimulate progress in the 
direction of making new discoveries and improvements. Therefore, in 
my reply to the somewhat lengthy discussion of Mr. Freeman, I shall 
endeavor to confine myself mainly to answering the direct questions that 
he has propounded, and to replying to a number of his adverse criticisms 
that I consider were based upon misapprehensions, which, if I have 
surmised correctly, may very probably have been owing to his not having 
had a sufficient length of time at his disposal to make a thorough exam- 
ination of my paper. 



84 DISCUSSION OK ELOW OF WATEK IN" PIPES. 

In reply to the remarks of Mr. Freeman (page 74), which commence 
thus: "It seems to me that Mr. Weston is off the true road toward a 
thoroughly satisfactory formula," * * * * and end thus: * * * * 
1 ' In one case his variable co-efficient is a function of only the diameter 
as a variable, in another of only the velocity, and in another of both the 
diameter and the velocity " — I will say: First — What I'have already inti- 
mated in my reply to the discussion of Mr. Hering, viz. : th&t I was 
governed by the experimental data that I possessed, and that the first 
preliminary investigations that I made relative to constructing a formula 
were to see if one could not be formed that would be sufficiently broad 
and general in its application to cover all kinds of pipes, and which 
would contain a factor dependent upon the roughness of the interior 
surface of the pipe. I was soon convinced, however, that a reliable 
formula of this kind could not be constructed. Second — That it strikes 
me the application of the formulas that I have recommended are just 
the reverse of narrow, as one of the formulas can be applied to all pipes 
having very smooth interior sides, from J-inch to 3£ inches in diameter 
(pipes of this kind larger than 3£ inches being very rarely used for con- 
veying water), and the other formula can be applied to all pipes having 
interior sides similar to new cast-iron pipes. Third — That a careful ex- 
amination of my paper will show that I recommend the latter formula 
(Darcy's) on account of its conforming closely to experimental results, 
and for its simplicity and not for its particular form. Fourth — That the 
other formulas that I have constructed, that have been mentioned in my 
paper, were computed from a limited number of experimental results 
and were not recommended for general use. 

In response to that portion of the discussion of Mr. Freeman (page 
75), which commences thus: "While discussing the desirability of includ- 
ing a special co-efficient of roughness in our future formula," * * * * 
and ends thus : * * * * " Nearly all of the five hundred experi- 
ments tabulated and discussed by Mr. Weston are these tabulated with 
the Kutter co-efficient of roughness conrputed for each" — I will state that 
in my opinion there are reasons for thinking that it would be question- 
able to apply the " Kutter formula" to pipes in which water was flowing 
under pressure, as this formula was constructed from experiments that 
were made with water flowing in open channels. But assuming that in 
special cases " Kutter's formula " was adapted for the purpose, and that 
the tabulated experimental co-efficients of roughness mentioned by Mr. 
Freeman were available, the results that would be obtained by using 
these co-efficients in this complicated formula would not be more accu- 
rate, and the opportunities for exercising personal judgment as to the 
relative degree of roughness of the interior surface of the pipes more 
facilitated, than they would if Table No. 1 of my rmper was referred to, 



DISCUSSION ON FLOW OF WATER IN" PIPES. 85 

in which each class of experiment is specified, and an exjjerimental 
co-efficient of friction (£) selected and used in the simple formula, 



a 

In reply to Mr. Freeman's advocacy of the Qhezy formula, I would 
call attention to pages 4, 5, 6 and 7 of my paper, where I discuss the 
form of formula the best adapted for the flow of water in pipes. 

I will say in reply to the remarks of Mr. Freeman (page 78) relative 
to the forms of formulas that I have given on pages 6 and 7, that the 
values of the co-efficients of friction (Q that are included in these 
formulas do not necessarily depend upon the velocity (v), even in the 
first formula of each example which is arranged for computing the velocity 
for a given head, as co-efficients to friction Q derived from " Darcy's 
formula," an expression for which I have given on pages 57 and 61, can 
be used and the velocity determined without approximation ; also when 
high velocities enter into the problem, there will be but little need of 
approximating when using co-efficients of friction (C) ■ dependent upon 
the velocities that have been determined from the majority of known 
formulas, as their values change very slowly after reaching a velocity of 
5 feet per second. Then the second formula in each example is arranged 
for computing the loss of head due to friction [hf), and can be directly 
solved ; even if co-efficients of friction (£), dependent upon the velocity, 
are used as in these cases, the velocity in the outlet pipe or pipes is one of 
the known quantites, from which, in cases of branch or compound 
pipes, the velocities in the other pipes can be readily determined and 
co-efficients of friction (C) selected corresponding to them. 

In respect to the co-efficients of resistance due to contraction (0), 
mentioned by Mr. Freeman (page 78), my reply to Professor Merriman's 
discussion expresses my ideas upon the subject. 

■ The reason why I did not plat upon the diagrams of my paper the 
results of the conclusions of Mr. Smith, given in his work referred to by 
Mr. Freeman (page 79), is, that my investigations were relative to 
formulas for the flow of water in pipes, and Mr. Smith only gives 
graphical results, and not formulas. 

In reply to the statement of Mr. Freeman (page 79), viz.: "Mr. 
Smith used substantially the same data as that from which Mr. Weston 
satisfied himself that the Darcy formula was satisfactory, and came to 
a different conclusion" * * * * — I would call attention to the 
diagrams from No. 14 to. No. 22, inclusive, which express very plainly 
my reasons for recommending the formulas of Darcy for new cast-iron 
pipes. 

In regard to my experiment with the 1-iuch pipe mentioned by Mr. 
Freeman (page 80), I will remark: First — that the condition of the in- 



86 DISCUSSION ON FLOW OF WATER IN PIPES. 

terior surface of the pipe, with the tin bushings in place, was about the 
same as the interior surface of an ordinary lead pipe, as I have already 
stated. I came to this conclusion by a careful examination of the differ- 
ent lengths as they were joined together while being laid. Second — that 
there is a possibility that the data given in Table No. 1, relating to this 
experiment, may be in error to the amount of 1 per cent. Third — that 
the loss of head in the f-inch tap was determined as follows : A short 
piece of lead pipe was soldered to the tap, before the 1-inch tin-lined 
pipe was connected, and a loss of head ascertained due to the discharge 
under the reservoir pressure, by measuring the flow. This loss of head 
was then compared with a diagram that had previously been constructed 
from the results of experiments, which covered a wide range of velocities, 
that had been made with other taps of the same kind connected to other 
main pipes, and as it agreed almost exactly with the law that had been 
developed upon the diagram, a loss of head was scaled from the diagram 
corresponding to a velocity of 6.03 feet per second, which was the velocity 
in the 1-inch tin-lined pipe during the experiment. The loss of head 
thus obtained was then added to the head required to generate the 
velocity and their sum subtracted from the total or reservoir head, the 
result of which is given in table No. 1 as the loss of head in the 1-inch 
tin-lined pipe. A considerable difference in judgment, however, one 
way or the other, in determining the loss of head in the &-inch tap, etc., 
would not have materially affected the results given in the table, owing 
to the small proportion that it would bear to the total loss of head, on 
account of the long length of the 1-inch tin-lined pipe; consequently, I 
did not consider the method followed in obtaining it of sufficient im- 
portance to be described in detail. There was not any measurable loss 
of head in the 36-inch main to which the f-inch was connected — about 
5 000 feet from the reservoir — as the only water moving in it at the time 
(the main being full and under the reservoir pressure) was the small 
quantity that was used in making the experiments. 

I will answer Mr. Freeman's questions relative to the possible error 
of my experiments, made with a 6-inch pipe, as follows: 

(a.) The gauges, which were very reliable, were tested a short 
time before the experiments were commenced with a mercurial 
column, and directly before and after the experiments with a large 
test gauge that was kept especially for the purpose, and which had 
also been tested a short time before the experiments were com- 
menced with a mercurial column. The dials of the gauges were 7 
inches in diameter, graduated to k pounds, and read from to 100. 
The gauges were each observed at least twenty minutes during each 
experiment. 

(b.) I do not think there is a question of doubt but that the 
piezometers were free from air, as great care was taken to blow 



DISCUSSION ON FLOW OF WATER IN PIPES. . 87 

them off before each experiment, and they were always full of water 
under pressure. 

(c. ) The piezometric orifices were exactly flush with the interior 
surface of the pipe, and normal to its axis. 

(d. ) The diameter of the pipe given in Table No. 1 is the ' ' foundry 
size," as it was not possible under the circumstances, the pipe being 
under ground, to measure the diameter ; but the pipe was exceed- 
ingly well made, it having been furnished by one of the best foun- 
dries in the country. 

(e.) It is almost absolutely certain that the pipe did not contain 
any obstacles like bunches of lead, etc., as each length of pipe was 
carefully inspected while being laid by a careful and experienced 
inspector. From what I have seen by examining pieces of other 
pipe of the same kind, that have been cut out while making repairs 
or connections and which had been in service about an equal length 
of time, in Providence, where the experiments were made, I should 
say that it was probable that the interior surface of the pipe was 
not quite as smooth as when the pipe was laid, owing to tubercles 
that may have formed at odd places when the coal-tar coating may 
have been thin. 

(/.) The lengths of hose were those that had been gauged. 

I have long recognized what Mr. Freeman states, viz. : "that eternal 
vigilance and everlasting patience are the price of scientific accuracy in 
this class of work." 

In reply to the comments of Mr. Freeman (page 81), which commence 
thus: "The experiments selected by Mr. Weston in developing his 
formula for very smooth pipes are in some respects questionable," 
■*•*** and end thus : * * * * " Moreover, in each of these 
cases of Rennie's and Neville's experiments the co-efficient of influx 
which has to be guessed at exercises a proportionately larger influence 
on the total loss of head than for longer pipes" — I will say : First — 
that the data of the experiments, from No. 1 to No. 14, were considered 
reliable by such an eminent authority as Professor Weisbach, from one 
of whose works I obtained them, as I have before mentioned, and that I 
was not able to secure any other information concerning them than 
what I have given in Table No. 1. Second — that Mr. Freeman is in error 
when he insinuates that I made use of Rennie's experiments in develop- 
ing my formula, as I only used these experiments for comparison after 
the formula was constructed, as may be seen in Table No. 1, and upon 
Diagrams Nos. 1 and 7. TJiird—tk&t the co-efficient of influx was not 
guessed at that was used with Neville's experiments, as a co-efficient was 
determined by experiment by Neville especially for these cases, as I have 
already stated. Fourth — that I take exceptions to Mr. Freeman's idea 
relating to the regimen of flow not being fully established in the pipes 



88 DISCUSSION ON FLOW OF WATER IK PIPES. 

that were used by Neville and Rennie in making their experiments. 
Such might have been the case if the velocities had been very low, but 
as the velocity of flow in the pipe used by Rennie was not less than 2.35 
feet per second, and the velocity of flow in the pipe used by Neville not 
less than 14.58 feet per second, I do not think there is any question but 
that the regimen was fully established. As bearing upon the subject, 
I will state that I have found in experimenting with a J-inch pipe, 6 feet 
in length, that with as low a velocity as 0.90 feet per second, the outlet 
end of the pipe was flowing full and the water running clear. 

In answer to Mr. Freeman's remarks (page 81), which commence 
thus: " For exact scientific purposes it seems hardly fair to class on the 
ground of smoothness experiments on new wrought-iron lap-welded 
gas pipe, f inch and 1 inch in diameter, along with the pipes of glass 
and lead," * * * * and end thus, * * * * "Give a much 
greater friction loss than a smooth lead pipe, and cannot properly be in- 
cluded " — I wish to say: First — what I have previously stated on page 
49, viz. : That the experiments that were made with the new wrought-iron 
gas pipe, mentioned by Mr. Freeman, were not given the same weight in 
the investigations as those that were known to have been made with 
pipes having very smooth interior sides, but were more especially used 
for the purpose of substantiating the laws and results obtained with the 
latter. Second— that I did not make use of Darcy's experiments which 
had been made with a new 1-inch wrought-iron pipe in the same manner 
that I did those of Smith, for the reason that I was well assured that 
wrought-iron pipes manufactured in France at the time Darcy made his 
experiments were not as well made, nor did they have nearly as smooth 
interior sides, as the gas pipe manufactured at the present time. Third 
— that I did not use in determining my general formula for pipes having 
very smooth interior sides, as I have stated on page 49, the experiments 
of Darcy that were made with riveted sheet-iron pipe, 7.40 inch and 
11.69 inch in diameter. 

In reply to the statements of Mr. Freeman (page 81), which com- 
mence thus: "It is hardly following the true scientific method, but is 
arguing in a circle," * * * * and end thus, * * * * "Was 
apparently merely the nominal or commercial diameter" — I will say: 
First — that as the nature of the pipe used in making the two experi- 
ments, Nos. 58 and 237, was questionable, I gave myself the benefit of 
the doubt, knowing that these two experiments would not appreciably 
influence the results which I should obtain, owing to the large number 
of other experiments that were used, which were made with pipes 
known to have very smooth interior sides. Second— that I have stated 
on page 49 that the data obtained from the experiments from No. 124 
to No. 139 were not given the same weight in the investigations as the 
data derived from experiments that were made with pipes having very 
smooth interior sides: 



DISCUSSION ON FLOW OF WATER IN PIPES. 89 

I will say in reply to the following remarks of Mr. Freeman (page 
81): "It may be of interest to note that the experiments of Leslie on 
2|-inch lead pipe (Nos. 250 to 269), and of Provis on 1^-inch lead pipe 
(Nos. 175 to 211), though referred to by Mr. Smith, are by him excluded 
from his results as unreliable "—First — that I think I was justified in 
using the experiments of Leslie and Provis as I did, more especially the 
former, as I made particular inquiries of Mr. Leslie in regard to them. 
Second — that if the descriptions that I have given are not sufficiently 
convincing as to the value of these two sets of experiments, I would sug- 
gest to those who are specially interested in the subject that they ex- 
amine the original papers that were written by these two experimenters. 

In reply to this question of Mr. Freeman (page 82) : * * * "Did 
the experimenter clearly understand the disturbing influence of air 
bubbles, and were they driven out and excluded with positive cer- 
tainty?" — I will remark that the impression that I have derived by 
reading Darcy's description of his experiments is, that he decidedly 
knew what he was about. 

To the following statement of Mr. Freeman (page 82): "As we thus 
carefully examine the quality of the data we see how unsatisfactory 
much of it is as a foundation for a new formula for very smooth 
pipes, and how very few are the really reliable experiments " — I will 
reply by saying that I think Mr. Freeman is decidedly wrong 
when he makes the assertion that very few of the experiments upon 
which I have based my new formula for very smooth pipes are really 
reliable, as I maintain that the reliability of the greater part of them 
should not be questioned, and I think a careful examination of my 
paper will prove that I am right in this respect, even if I have failed to 
show that the majority of Mr. Freeman's exceptions to my work, that 
he has mentioned in detail in his discussion and which I have pre- 
viously replied to, are unwarranted. 

I do not consider Mr. Freeman's comparison (page 82) of surveying 
a field with the making of hydraulic experiments, a fair one, and I am 
somewhat surprised after his recent experience in making extensive 
experiments with fire hose and nozzles,* that he should suggest such a 
comparison ; and I can assure Mr. Freeman, from the results of my own 
experience, that if I could have made experiments relating to the flow 
of water in pipes as easily and with as little expense as I could have 
surveyed a field, I should not have given him or any other member of 
the Society an opportunity to criticise any experiments other than my 
own. 

I will conclude by remarking, as Mr. Freeman has referred to tables 
relating to the flow of water in pipes (page 83), that I have appended to 
my paper in convenient form for platting, a short table that has been 

* Transactions, Vol. XXI. No. 426, November, 1889; " Experiments Relating to Hydraulics 
of Fire Streams," by John R. Freeman. 



90 DISCUSSION ON" FLOW OF WATER IK PIPES. 

calculated from my new formula for the now of water in very smooth 
pipes. And that a table for the flow of water in new cast-iron pipes that 
was computed under my direction from Darcy's formulas, which is 
similar to the table mentioned by Mr. Freeman, though more complete, 
may be found in the appendix to the Report of the City Engineer of 
Providence, for the year 1888. I would also call attention to two other 
convenient tables relating to the same subject, one of which is calculated 
from Weisbach's formula, and is included in the discussion of a paper by 
James Leslie in the " Excerpt Minutes of Proceedings of the Institution 
of Civil Engineers, Vol. XIV, Session 1854-55," and the other is ap- 
pended to a " Rudimentary Treatise on Civil Engineering, by Henry 
Law, C. E.," that was published in London, by John Weale. 




021 626 155 



